Preheat broiler. Arrange the fillets in a baking dish. Sprinkle with the salt and pepper. Place 2 sprigs of dill, 3 lemon slices, and 1 tablespoon of butter on each piece of fish. Broil until the fish is just cooked and is flaky and opaque, 10 to 12 minutes. Toss the warm rice with the remaining butter and the zest. Spoon the rice onto dinner plates and top with the fish. Serve with steamed cabbage.