Set oven rack 6 inches from broiler. Line a sheet pan with foil and place a rack on top.
Preheat the broiler on high.
Butterfly the tails: cut shells lengthwise, loosen meat, and lift to rest on top of the shell.
Pat the lobster meat dry with paper towels.
Whisk melted butter, lemon juice, garlic, paprika, salt, pepper, and cayenne.
Brush half the butter mixture over the exposed lobster meat.
Broil until meat is opaque and lightly browned, 6–8 minutes, rotating the pan halfway.
Baste with remaining butter and broil 30–60 seconds more to glaze.
Rest 2 minutes, sprinkle with parsley, and serve immediately.