I learned this dish from a youtube presentation by Madhur Jaffrey. The youtube video references her book "Vegetarian India: A Journey Through the Best of Indian Home Cooking." However, that book actually presents a different variant, one without coconut milk.
Clean and cut the mushrooms, quartering large ones and cutting small ones in half. Thoroughly rub the salt and turmeric in. (This will stain your hands, so you can use gloves if you're concerned. It will also stain plastic.) Let the mushrooms sit for 10 minutes or so. The mushrooms will soften a little and absorb some flavor from the turmeric.
While the mushrooms sit, heat the oil. Add the mustard seeds and let them pop. Once they finish popping, add the shallots and fry them over medium-high heat until they begin to brown.
Remove from heat to avoid scorching the powdered spices. Add the chili powder and stir to mix with the oil. Cook for a bit until everything is well mixed.
Return to heat at medium-low. Add the green chilis and cook until softened.
Add the mushrooms, increase heat to medium-high, and fry for about two minutes.
Open the coconut milk and skim off the thick cream. Add 3/4 cup of thin coconut liquid to the mushrooms and cook for about 10 minutes to reduce.
Reduce the heat. Add 3/4 cup of the coconut cream and simmer gently over medium-low for about one minute.
Finally, turn off the heat completely and stir in the lime juice.
I added the mustard seeds by accident–I misremembered them from a different dish. For now I'm leaving them in the recipe, since I liked them.
Jaffrey's recipe called for only 1 pound of mushrooms along with 1 teaspoon of salt "to taste." But since the salt is used right away to soften the mushrooms, it's impossible to scale back later. I found the results overly salty so I'm trying 1/2 teaspoon. I also found that one can of coconut milk can accomodate a few more mushsrooms quite comfortably. I suppose the coconut milk could be reduced more, but I like it this way.
Update: 1/2 teaspoon was distinctly too little! Maybe I mismeasured the time it came out salty? Maybe I need to adapt it to the mushrooms. I guess this is still a WIP.