I made some Thai red curry a few days ago. It turned out pretty well. The only problem is that it was fairly runny. I thickened it up with a slurry which helped a bit. I doubt a roux would have any more thickening power. I'm sure there's got to be a better way. Thanks in advance!
First, start your Thai coconut curry sauce in a separate pot (i.e. the coconut milk and later the seasonings; no meat , no vegetables, etc.). Make sure to shake the can of coconut milk before opening to ensure it is not separated. Add 1/2 the can to the pot. Bring to boil, reduce temperature and allow the mixture to reduce to almost a paste like texture. This will allow the coconut flavors to intensify, and give you a thicker starting point.
The key is to reduce some of your sauce before cooking everything else; if you attempt to reduce your entire sauce with the vegetables, they will overcook because the process takes too long. Once reduced, add the other 1/2 of the coconut mixture. You end up with a very silky, smooth coconut sauce. Afterwards add your curry paste, fish sauce, sugar, Thai basil etc.
When you open a can of coconut milk, it usually has separated, with the thick stuff at the top, and more watery business at the bottom. Don't shake or stir it! Start your curry with just the thick stuff, and then thin it as needed with the remainder. I would definitely not add a starch-based thickener. That isn't traditional in Thai curries and will inevitably make them a little gloopy.
A runny curry means you haven't cooked it long enough and/or you have used coconut milk with a low percentage of solids. Authentic curries never contain any type of starch (flour).
So, buy coconut milk (or cream) with the highest percentage of solids that you can find. Next, use more paste. If you are happy with the spice level and you still need more paste you can add bell peppers to the paste. Match colours of course. This will make the paste a little more watery but it'll still work very well.
Last of all, use a better curry method to cook it.
Best way to thicken is is to grate a potato or two in there. Potato is delicious in curries and adds creaminess naturally.
I also like to turn some dry coconut flakes to powder using a coffee grinder and add it in. It intensifies the coconut flavor and thickens at the same time.
Lastly, the mother of all coconut curry thickeners is coconut flour. You can find it in some grocery stores or on Amazon.
Rice flour does the trick too. Curry is eaten with rice so why not thicken it with rice flour?