Prep lobster tails by using scissors to cut lengthwise down the shell. Cut towards the tail, stopping before the end to keep the tail connected. Using your fingers, push inside the shell to loosen the meat, then gently push the meat up through the butterflied shell. Place on a baking tray.
Mix butter, salt, pepper, and paprika in a small bowl then use a pastry brush to coat the meat of each lobster tail.
Set broiler on low and place tails on highest rack in oven for approximately 5-6 minutes. Remove tails and brush with more of the butter mixture. Set broil to high and continue to cook tails for another 6-7 minutes until they are completely opaque and browned in places on top.
While the tails are cooking, in a saucepan over medium heat, add the olive oil and garlic. Sauté until fully softened, but not browned.
Add the vegetable broth, lemon juice, and heavy whipping cream. Whisk until a low simmer, then remove from heat.
Plate the lobster tail drizzled with lemon cream sauce and served with lemon wedge and chopped parsley.
