How to Make It
In a small bowl, whisk the coconut milk with the curry paste and fish sauce until combined.
Heat a large wok or skillet until very hot. Add 2 tablespoons of the vegetable oil and heat until just smoking. Season the chicken with salt and pepper and add it to the wok in a single layer. Cook over high heat, turning once, until the chicken is browned but not cooked through, 4 to 5 minutes. Transfer the chicken to a plate and pour off the fat in the wok.
Add the remaining 1 tablespoon of vegetable oil to the wok. Add the shiitake caps and stir-fry over high heat until lightly browned, about 5 minutes. Add the ginger and garlic and stir-fry for 1 minute. Return the chicken and any accumulated juices to the wok. Add the red curry mixture and the water and bring to a boil. Add the frozen peas and simmer until the liquid is slightly reduced and the peas are warm, 2 to 3 minutes. Transfer the chicken curry to a serving bowl and garnish with peanuts and cilantro. Serve immediately with rice and lime wedges.