I have no idea what a "typical" Stroganoff is. As it became popular (or possibly as Russians emigrated to other lands) it evolved into more variations than there are on Paganini's theme! For me, if it contains anything beyond beef (never tenderloin!), onions, mushrooms, butter (the real thing!), salt, pepper, sour cream and a touch of nutmeg, then it's not "authentic" beef Stroganoff.
I was taught to make Stroganoff in the late 1950s by the very ancient Russian family retainer of close friends when I lived in Turkey. Tensela had walked from Moscow to Istanbul with her husband in 1914 to escape the Bolsheviks and finally landed in the employ of the Basegmez family. Her first instruction to me on how to make beef Stroganoff was (roughly translated), "Forget about Count Stroganoff! He just loaned the dish his name. It's actually a very very old peasant recipe made by people who worked hard to grow their own food and meat, and wasted nothing!" Tensela's recipe was basically this:
1 kilo (roughly 2 pounds) of beef. Never use tenderloin or brisket. Any other cut will do, and leave at least some fat in. It adds to the flavor! Slice it bacon thin across the grain. The cross grain cutting is critical, otherwise you will end up with unchewable shoe leather. Tensela didn't teach me this, but I have found that partially freezing the beef is a great help in slicing it uniformly thin. Depending on the cut of meat you're using, you may want to do some cutting and customizing before partially freezing to make cutting across the grain easier. For example, I often use a seven bone roast, which is already sliced across the grain, so I buy as thick a roast as I can find, then cut it into sections shaped something like 1/3 of a strip of bacon. When I partially freeze and then cross cut those pieces, I end up with perfect beef for Stroganoff!
2 or 3 large yellow onions. No, not shallots! Remember the goal is to only use ingredients that would be available to a Russian peasant's wife in the 19th century! So you want globe onions. I don't like the bite of white onions, so I use yellow. And don't use purple onions. They're too darn ugly when cooked and floating in sour cream! Cut off the stem and blossom ends, then cut the onion in half, cut end to cut end. Lay on its flat side and slice across in about 1/4 inch slices.. The goal is to have something akin to "short onion spaghetti" when it's cooked. Put the onions in a bowl and set aside.
Mushrooms. If you're an expert on wild Russian mushrooms, use whatever you think is appropriate. I use standard button mushrooms. Don't get too exotic. But do your thing. Just DON'T use canned mushrooms! Save them for a canned goods drive. Slice the mushrooms "vertically" stem to cap. About a quarter to an eighth of an inch thick is good. As for how many mushrooms to buy? <sigh> I cannot tell you in pounds or ounces. The best I can do is tell you that you want a volume of sliced mushrooms equal to the volume of onions, which should be about equal to the volume of sliced beef.
Then you need BUTTER! Keep a lot of it handy. You use it as needed.
Sour cream... a large container of real sour cream, no imitations, and as few ingredients as possible. Maybe have an extra container on hand just in case.
Kosher salt, but sea salt will work too. Just leave the iodized round box salt in the cupboard. It wasn't around in Russian farm kitchens of the 19th century!
Nutmeg, preferably whole nutmegs you grind, scrape or shave yourself.
Black pepper is optional.
Before doing anything else, dump the sour cream in a bowl and stir to reliquify, then let it set out while you do the following:
I use my big old 12" cast iron skillet. Heat it to medium hot, melt a generous lump of butter, dump in the onions, stir, reduce heat and cover, stirring occasionally until onions are soft and transparent. Remove the onions to a large bowl.
Heat pan to medium hot again and add more butter if needed to saute the beef. Remember, "saute" means to jump and you want to very quickly brown the meat (a little pink is fine) in the onion flavored butter. DO NOT crowd the pan! It is better to do the beef slices in several batches than it is to make beef soup with its own juices! When just reaching the "browned" stage with a bit of pink still showing, remove beef to bowl with onions. Cross cutting the beef and cooking lightly are both steps to promote tenderness in the final dish. Overcook this beef (easily done) and you will diminish the flavor and make it tough.
When all of the beef is done, add more butter to the pan and dump in the mushrooms. No standing on ceremony here! They could care less about being crowded. Reduce the pan heat, put a lid on them, then check regularly on whether they need more butter. Mushrooms drink butter like an unrecovered alcoholic chugs free beer! But you don't want to oversaturate them either. Cook them until they are the tenderness/texture you want in the final dish.
When the mushrooms are done to your liking, return the onions and beef to the pan, salt lightly and tossr to mix everything together. Turn off the heat. Stir in the sour cream. Do NOT allow it to boil or it will curdle! It will still be taste good, but if this happens you'd better blindfold everyone before serving. It turns really ugly when curdled! Stir gently. The sour cream will pick up coloring and flavor from the pan and the contents.
When nicely blended, taste and add more salt if needed, and a dash of nutmeg. You're not making egg nog, so don't overdo it! Nutmeg is an interesting spice with a long history in Europe as the best way to disguise spoilt meat. Remember, they didn't have refrigerators! For the Stroganoff, you just want to use a touch. Enough that people will wonder what that unusual flavor is but not be able to taste it well enough to guess.
Serve immediately over buttered egg noodles. "More butter?" you ask. Hey! XIX Century Russian peasants ONLY had grass fed beef, grass fed butter, grass fed yogurt. That kind of cholesterol content rivals wild caught salmon! Omega 3s and all that good stuff. So if you want a really authentic pre-Count Stroganoff dish, use grass fed! Of course, that will up the price a bit, but think what you will have gained!
You can use a light sprinkle of finely chopped parsley as a garnish on the plated dish. Instead, I use fresh coarsely ground black telecherry pepper. I have served this from a chafing dish for parties, but be sure the alcohol burner or candle isn't too hot.
Oh, and for the record, I don't think XIX Century Russian serfs grew tomatoes and it was a hell of a long way to Safeway! '-)
My native Russian family makes beef stroganoff like this: saute sliced onions, mushrooms if you like but are optional, then saute thinly sliced round steak, add all together, season with salt and pepper and then squirt some ketchup in, mix all well. Add sour cream (Russian sour cream is more liquidy than American) and mix well, do not boil it just warm it. Serve with fried potatoes. Yummy! (No one realizes it is ketchup that is adding such a nice flavor).
Never seen or heard of tomatoes in Stroganoff, but I'm not going to argue with Larousse. More important, to my mind, is the quality and preparation of the beef - it has to be top-quality sirloin or tenderloin and barely seared. Too often (even in Russian restaurants!) I've been served "Beef Stroganoff" that's really long-cooked beef stew.