enriching thai curry with milk?

Growing up, my mom (Italian-American) would make curry using a bechamel-like white sauce plus curry powder. She said it was her mother's recipe, and I can only assume it was attempting to recreate a meal that she had using ingredients and techniques that she knew.

There are is an advantage of using a white sauce over using just cream to enrich the sauce -- the starch will keep the sauce from breaking over higher heat, but it can get a bit too thick and keep the other flavors from really coming through if you make it too thick, and I don't know if the flavors meld the same way as with coconut milk. (it's been years since I've had this dish, and I currently avoid dairy)

I've never tried mixing bechamel to something that already had coconut milk ... but I suspect that it could work. I know that I've made a white sauce using vegetable molks before (almond & soy ... coconut is the wrong consistency on its own, but there's 'coconut milk drink' that might work, or you could try thinning it with water)

Milk is not an ingredient I think of with Indian recipes, nor would it enrich your curry. It isn't very rich, all you will do is water it down. Bechamel is also not part of any indian recipe I've ever seen.

Yogurt is what you are looking for if you don't want to use ghee (and I can't blame you on that one), although you can make your own clarified butter without too much trouble. Yogurt is used widely in indian cuisine and does add a rich quality. I wouldn't add oil or butter substitute, you'll end up with a greasy dish.

Thai and Indian curries differ in flavors because of spices, that deep flavor you are looking for is from the spices more than the base. Indian and Thai both use turmeric, cumin and coriander widely, however Indian curries can use cardamom, black mustard, yellow mustard, fenugreek seeds or leaves, black pepper, asafoetida, nigella seeds, bay, and many more I cannot think of. The combinations used vary widely depending on the region. Try some and see what you think, just remember that the powders should be fried in a bit of oil for a 60 seconds to get their flavors out.

If you don't remove coconut milk when you add cows milk, you will water the dish down too much. However you can still add the creamy part of the milk if you wish, keep reading if interested.

If you wish to add milky creamy richness I would use marscapone. It will thicken your dish and give you that creaminess without altering the flavor of the recipe like milk cultures can (yogurt, sour cream, etc). a 16 ounce tub costs about $10-16 depending on where you are.

Marscapone is also very easy to make if it's not available at the store or you want to save some moeny. 1 qt heavy cream, gently bring to 180 F in stainless steel sauce pan (it's almost there when the cream starts to get frothy when stired), stir in 3 teaspoons of lemon juice, keep stirring. Cream will start to firm up a little bit.

Put the whole pot in the refrigerator overnight. In the morning you have a wet marscapone. You can use that if desired, or you can drain it by hanging it up in a sterile handkerchief tied together at the 4 corners and hung up, and letting the whey drip away.

Within 24 hours from start to finish, with $3 worth of ingredients you have a $16 tub's worth of marscapone that will add the creaminess you desire without adding more liquid to your dish.