To thicken, you would mix in an agent designed to do so. There are many options, but here are some that are directly applicable to Asian cooking:
Corn starch - Works well in small quantities, though I find it has a tendency to turn sauces into jello in the fridge. If you have too much liquid in your sauce and use a relatively large amount of cornstarch, you can have unusual effects when trying to reheat the leftovers. Specifically, cornstarch solutions can suffer from shear thickening making it hard to return a gelatinized corn starch sauce to liquid form. However, this is 'authentic' in the sense that it is probably what is in your neighborhood General Tso's purveyor's recipe.
Xanthan gum - Works well in very small quantities; it doesn't take much to thicken a sauce. I don't think there is anything very Asian about this ingredient, it's more of an 'industrial' food additive. Still, it is flavorless so won't impact the taste of your sauce. Xanthan gum has the opposite effect of cornstarch, namely shear thinning. I don't find the shear thinning to be an undesirable trait.
Potato or Tapioca starch - These are my personal preference. These starches act more like flour, in my opinion, and since I have more of a cooking background with gravies and roux, I like these options. To a certain extend, you will have the same shear thickining effect that you will get from corn starch, but I've never gelatinized a sauce with either of these ingredients, so that drives my personal preference.
The above listed don't need more than a few minutes at heat to achieve their thickening effect. Be sure to stir in completely and be patient; if you add thickening agents in haste you can easily end up with too much (again, I find this to be a big problem with cornstarch). Also, for all of them, be sure you don't have too much liquid in the first place; a sea of sticky sauce can often be overpowering.
There are plenty of other thickening agents in common use (flour/roux, egg whites, pectin, gelatin). You could give any of these a try, but I wouldn't consider them "Asian" in any way, so I don't feel like these answer the question.