Prepare the lobster tails: Use kitchen scissors to cut through the top shell of each lobster tail, stopping at the base and snipping through the top portion of the meat as you go.

Crack and butterfly: Flip each tail over and crack the ribs in the center to help open the shell. Carefully open the shell using your thumbs and fingers, loosening the meat from the shell. Remove any gray vein if present. Lift the meat from the shell while keeping it attached at the base, then press the shell together and set the lobster meat on top.

Prep the oven: Position the oven rack in the center so lobster tails will be at least 6 inches from the heating element. Preheat oven to broil on high heat.

Make the marinade: In a small bowl, combine parsley, garlic, Dijon mustard, salt, pepper, olive oil, and lemon juice. Stir well to combine.

Prepare for broiling: Place butterflied lobster tails in a 9x13 inch baking dish, flesh-side up. Divide the marinade evenly over the tops of each tail and dot each with 1/2 tablespoon butter cut into small pieces.

Broil the lobster: Broil on high heat for 10-11 minutes (adjust time based on size - see notes). The meat should be opaque and white in the center and register 145°F on an instant-read thermometer.

Make garlic lemon butter: Transfer lobster tails to a serving platter. Drain pan drippings into a small saucepan and combine with remaining 2 tablespoons butter. Bring to a simmer and remove from heat.

Serve: Pour the garlic lemon butter over lobster tails or serve in small ramekins as dipping sauce. Garnish with fresh parsley and serve with lemon wedges.