Rinse fish and pat dry. Baste the grill rack with clarified butter. Break the eggs onto a platter and mix with the clarified butter to form an egg wash for the fish. Preheat the broiler. Dust the fish with flour. Brush with egg wash on both sides. Place under broiler and broil for 5 minutes. Remove from the oven turn the fish over and brush and brush with egg wash. Return to the broiler and broil until golden brown. Remove the shell and then the sand track from the shrimp and cut them in half lengthwise. Wash the mushrooms, dry and cut into 1/2-inch slices. Saute shrimp and mushrooms a few minutes in a hot pan coated with a little clarified butter. Squeeze about 2 teaspoons of lemon juice over the mixture and sprinkle with salt and pepper. Add 2 ounces Sherry and ignite. Wash, dry and chop the chives. Add to shrimp-mushroom mixture.
Blend the 2 teaspoons of salted butter with the 2 tablespoons of flour to form a "Beurre Manie." Add butter-flour mixture to the pan and stir until well combined. Heat a serving platter. Slide fish onto platter, cut in half from the head to the tail and pour shrimp-mushroom sauce over fish.
Shrimp atop a broiled Pompano