How do I cook bulgogi without getting a lot of burnt sugar soon after ?
Every recipe I've seen has enough sugar to burn very quickly before the batch is complete or at least to make a serious burnt bits mess.
Is the meat sliced thinly enough? I've never burnt bulgogi, but the key is to make sure it cooks before it burns. If you're not getting really thin meat, then find a new butcher or partially freeze it and slice it yourself to make sure.
Meat for Bulgogi should be sliced less than 1/4 inch thick which means it cooks very quickly.
I have cooked it as stir fry, on the grill, in a hot skillet, under the broiler, and have never had a problem unless I just space out and let it go.
In stir fry the marinade and meat juices provide enough of a sauce to prevent burning, on the grill or under the broiler the meat should be thoroughly cooked in just a couple minutes.
Frying in a skillet can be a little tricky, but if you do not overcrowd (just a few pieces at a time) the meat will be done before burning. (use one or two pieces to "mop" the skillet before the next batch)