In a small bowl, whisk the coconut milk with the curry paste and fish sauce until combined. Heat a large 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 skillet 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 skillet. Add the remaining 1 tablespoon of vegetable oil to the skillet. Add the shiitake caps and stir-fry over high heat until lightly browned, about 5 minutes. Stir in the ginger and garlic, stir-fry for 1 minute. Add the chicken, red curry mixture and the water and bring to a boil. Reduce heat and simmer for 2 to 3 minutes or until the chicken is cooked through. Transfer the chicken and curry sauce to a serving bowl and garnish with peanuts and cilantro. Serve immediately with rice and lime wedges.