Your closest quality ramen fix would be Santouka in the Mitsuwa Market food court. By any standard, they are very respectable. It will be similar to Hakata-style ramen - pork bones in the broth, but there's a nice subtle sweetness from a dashi-type stock as well. You'll choose between shoyu, miso or shio ramen. I think most opt for the shio - it's the classic there. But the ramen comes in a choice of bowls in three different sizes. You and your Husband can order all three in the smallest size and decide which you prefer from that point. Assuming you're used to large bowls of ramen, three smalls should fit nicely.
Those hirata buns are something I've only seen either in a Chinese supermarket or in a Chinese restaurant that serves duck. I'm only guessing, but I think Ippudo and Momfuku have taken these Chinese bao and made a hybrid app sandwich that is only their own. I personally don't know of an equivalent in LA, but it seems so easy to do on your own. The buns can be sourced at any Chinese market - the closest to Venice would be 99 Ranch Market in Van Nuys. The next closest would be 99 Ranch in Gardena. It's a smaller store and I'm assuming less turnover, so we prefer the Van Nuys branch. I don't know what the recipes are for the fillings (i.e. the pork), so someone else more worthy than me could chime in on that.
A very current thread by Chow Demigod poster exilekiss might be of interest to you. exilekiss would be the Chow equivalent of Derek Jeter. He does it all - excellent fielder, long ball, short ball, puts a good face on the team, and of course, the women line up just for a glance at the stud. :) Seriously, you'd be doing yourself a favor to click onto his link and a whole world of good food (mostly in SoCal) will open up to you.
This would be the perfect excuse to visit the Torrance area, which is Nippon-central for large numbers of Japanese expats. And if you want a taste of home, the Ippudo folks are at the food festival at the Mitsuwa located in Costa Mesa ( OC is another area quickly becoming hub for Japanese immigrants).
Today is the last day for the respective food festivals, and these festivals have a reputation of running out of food, so head down early and get in line...
3760 S Centinela Avenue, Los Angeles, CA 90066
I've never had those hirata buns, which look delicious. I'm hoping some of the Hounds who know 1,000 x more than me can chime in where else to source either the buns you're looking for, or good examples of Chinese dishes using those buns that are served around the area.
It seems pork is the common filling, while shrimp seems to show up as well. There are so many pork options that you can pursue if you want ready-made - seek those out in the more ethnic areas. Buta no kakuni (you can easily do this at home - just takes a little bit of patience), pork pump, carnitas, etc. Really nice cuts of pork can be had at places like Mitsuwa (Mar Vista) and Nijiya (West LA); for huge slabs, try Chinese markets.
An angle worth pursuing on the shrimp might be live shrimp at one of many Chinese markets. California spot prawns (on the smaller side) were the only offerings I saw at the San Gabriel 99 Ranch market yesterday ($14/lb) - I think those are far too worthy of being treated as a filling.
I can't think of anything in your area that is similar to Ippudo, both in terms of quality and style of ramen. Santouka, in the Mitsuwa food court at Centinela and Venice, is good, but it's a different style of ramen that uses thicker noodles.
The closest to Ippudo's ramen in LA would be either Asa Ramen or Hakata Ramen Shin-Sen-Gumi, both of which are in Gardena. Asa on a very good day is close in terms of quality (I think Asa's noodles are superior, but the broth is a notch below), but still a little bit different in style. SSG is closest in style, but the quality isn't as good. Neither have the same clubby ambiance as Ippudo.
No idea about hirata buns - they seem to be unique to Ippudo. Would Chinese char siu bao be even remotely similar?
3760 S Centinela Avenue, Los Angeles, CA 90066
18202 S Western Ave, Torrance, CA 90248
I suggest you scope out sawtelle blvd from Olympic to almost Santa monica - and olympic over to Ramenya. Don't know your new york restaurants. sorry. But there are quite a few places, izakaya, ramen hosues, udon places, etc. and you omight find something you like there.
also, if you take the freeway down about 20 minutes or so to Gardena, there's a world for you to explore - omakase tempura houses, okonomiyaki parlors, and even a place that makes it's own white soba with highgrade buckwheat.
11555 W Olympic Blvd, Los Angeles, CA 90064