Shell the shrimp, but be careful not to remove the tail. With a small sharp knife, slit each shrimp down the back and under and lift out the black or white intestinal vein. Wash the shrimp quickly under cold running water and pat them thoroughly dry with paper towels.

Preheat the broiler to its highest temperature. In a shallow flame proof baking dish or pan just large enough to hold the shrimp in one layer, melt the butter over low heat, and be careful not to let it brown. Stir in oil, lemon juice, shallots or scallions, garlic, salt and a few grindings of pepper, add shrimp and turn them in the butter and oil until they glisten on all sides.

Broil them 3 to 4 inches from the heat for 5 minutes then turn the shrimp over and broil them for 5 to 10 minutes longer or until they are lightly browned and firm to the touch. Be careful not to overcook them. With tongs, transfer the shrimp to a heated serving platter, pour the sauce from the pan over them and sprinkle with chopped parsley. Garnish with lemon quarters.