Pulse nuts in a food processor until finely ground. Add panko, and pulse until combined. Place mixture in a shallow bowl.
Place flour in a shallow dish. Whisk egg in a medium bowl. Sprinkle fish with salt and pepper. Dredge in flour, shake off excess, and dip in egg. Dredge fish in nut mixture, coating completely.
Heat 2 tablespoons oil in a large, heavy skillet over medium heat. Add 2 fillets; cook 3 minutes on each side or until golden. (If nuts brown too quickly, reduce heat.) Repeat with remaining 2 tablespoons oil and fish. Divide rice and fish fillets among 4 serving plates. Top with Mango-Butter Sauce, and sprinkle with green onions.