Step 1

In a blender, combine the shredded coconut and warm water. Let stand until the coconut begins to soften, about 5 minutes. Blend on high until creamy, 1 to 2 minutes. Pour the mixture into a fine-mesh sieve set over a large saucepan. Press on the solids to extract as much liquid as possible; discard the solids.

Step 2

Using a vegetable peeler, remove the zest from the limes in strips; remove only the colored portion, not the white pith beneath. You will need a total of about 10 strips, each 2 to 3 inches long; add them to the saucepan. Juice the limes; you will need 3 tablespoons; set aside.

Step 3

To the saucepan, add the coconut cream, coconut water, lemon grass, ginger, shallot, turmeric, ½ teaspoon salt and ¼ teaspoon white pepper. Bring to a simmer over medium-high, then reduce to low and cook, uncovered and stirring occasionally, for 20 minutes. Remove the pan from the heat. Using a slotted spoon, remove and discard the solids.

Step 4

For oyster mushrooms, tear them into bite-size pieces. For shiitakes, stem and thinly slice them. Stir the mushrooms, then bring to a simmer over medium. Add the chicken, fish sauce, chili paste, sugar and ⅛ teaspoon white pepper. Simmer, uncovered and stirring occasionally, until the chicken is opaque throughout and the mushrooms are tender, about 5 minutes. Off heat, stir in the lime juice and sliced chili. Taste and season with salt or fish sauce and white pepper. Serve sprinkled with cilantro.