Preheat oven to 190 C / Gas 5. Grease a deep (2L) ovenproof dish.
Cook rice according to instructions on the package. Drain.
In a bowl mix together cooked rice, fish, lemon juice, chives, cayenne and cream. Stir well and season with salt and pepper to taste.
Sprinkle 2 tablespoons breadcrumbs evenly over base and sides of the greased ovenproof dish. Pack in about 2/3 of the fish and rice mixture and make a hollow in the centre for the eggs. Place quartered eggs in the middle and drizzle with melted butter. Layer with mozzarella cheese (optional), top with remaining fish and rice mixture, press down firmly to make a level top and sprinkle with the rest of the breadcrumbs.
Bake for 45 minutes, remove from the oven and let stand for a few moments. Turn onto a warm plate.