Bring the rice, 1 1/3 cups water and 1/4 teaspoon salt to a simmer in a saucepan over medium-high heat. Reduce the heat to low, cover and cook 15 minutes. Remove from the heat and add the peas; cover and set aside.
Puree 1/2 cup yogurt, the garlic, ginger, lime juice, cumin, cayenne and 3/4 teaspoon salt in a food processor. Transfer all but 3 tablespoons of the mixture to a large bowl. Pierce the fish a few times with a fork and season with salt; add to the bowl and toss. Marinate 15 minutes.
Preheat the broiler. Place the fish on a broiler pan; top with the marinade and butter. Broil until opaque, 6 to 8 minutes. Mix the remaining 1/4 cup yogurt, the cilantro, and salt to taste with the yogurt mixture. Serve the fish and rice with the yogurt sauce and lime wedges.