Cut down the top shell of each lobster tail with kitchen shears, stopping before the tail fin.
Gently lift the lobster meat from the shell, keeping it attached at the fin, and rest it on top of the shell.
In a small saucepan over low heat, combine 2 tablespoons unsalted butter, olive oil, pressed garlic, Dijon mustard, sea salt, black pepper, fresh parsley, and lemon juice.
Stir continuously until the butter melts and the garlic is fragrant, about 3 to 5 minutes, then keep warm.
Preheat the broiler to high and place prepared lobster tails on a broiler pan or baking sheet.
Brush the lobster meat generously with some of the garlic lemon butter mixture.
Broil the lobster tails for 8 to 10 minutes, until the meat is opaque and lightly browned, taking care not to overcook.
Remove from the oven and brush again with the remaining garlic lemon butter.
Garnish with additional fresh parsley and serve immediately with extra garlic lemon butter on the side.