Spicy Red Curry Chicken and Rice

Name: Spicy Red Curry Chicken and Rice
Ingredients: 2/3 cup unsweetened coconut milk; 2 to 3 teaspoons Thai red curry paste; 1 tablespoon Asian fish sauce; 3 tablespoons vegetable oil, divided; 1 1/2 pounds skinless, boneless chicken thighs, cut into 1/2-inch strips, or skinless, boneless breasts, cut into 1 1/2-inch chunks; Salt and freshly ground black pepper; 1/2 pound shiitake mushrooms, stemmed, caps quartered; 1 tablespoon very finely chopped fresh ginger; 2 large garlic cloves, very finely chopped; 1/2 cup water; Toasted peanuts and cilantro leaves, for garnish; Steamed rice and lime wedges, for serving