There is a range of techniques and some overlap of course.
The cuisines I'm weakest on are Korean, Japanese and Thai.
The Kimchi Chronicles by Marja Vongerichten (Jean Georges wife). The PBS series for this book was also quite good. Funny to see Hugh Jackman, and the Vongericthens cooking together, but they live in the same building.
China, you should look at these authors:
Eileen Yin Fei Lo-- Many books, none of them bad. Some overlapping content here and there, but plenty of knowledge.
Barbara Tropp--The Modern Art of Chinese Cooking has a good section on technique. Much less so her China Moon which should be skipped.
Bruce Cost-- Most of these are out of print, but he's quite an expert.
- Asian Ingredients--not as comprehensive as you could hope, but still useful
- Ginger East to West
- I like his "Big Bowl" as well, but it's not on topic so much.
Fuschia Dunlop is slowly writing excellent regional cookbooks for China. Her Shark's Fin and Sichuan Pepper is not for cooking.
Nina Simonds, more her earlier books than her more recent.
Kenneth Lo has written a great many Chinese cookbooks over the decades; these can be found used. Skip his books from the early 70s. These are mostly highly adapted to the limited ingredients available then. Interesting in their own right, but not what you're looking for.
- New Chinese Cooking School--pretty good intro to technique and ingredients
- Chinese Regional Cooking is taken mostly from restaurants in China and is full of things I've never seen anywhere else. This was written during the start of the transition to modern pinyin (When Peking became Beijing for example) so the transliterations are different than you might be used to now.
Phaidon recently released their China:The Cookbook. I've been pretty impressed with it.
--this blogger author has also released a worthwhile cookbook or two.
The Fortune Cookie Chronicles by Jennifer 8 Lee. Not a cookbook. More a look at Chinese American cuisine and it's facade. Very interesting.
Charles Phan Vietnamese Home Cooking
Andrea Nguyen writes the vietworldkitchen.com blog and has a few cookbooks. I was quite impressed with her Banh Mi book
Mai Pham, particularly Pleasures of the Vietnamese Table
I've never found a cookbook for Thailand that really helped me grok the cuisine, flavor and ethos so I could cook it more intutively. I'm still looking
I've read a couple of good ones, but own nothing and I don't recall specific ones to recommend. But there are some out there. Bee Yin Low does some from her heritage, often with some streamlining and other asian cuisine at rasamalaysia.com. Expect lots of streamlining in the recipes.
Just for my personal definition if nothing else, I don't include India as Asian cooking. It's rather different though there is some cross pollination.