• Gather all ingredients and tools.

Prepare Lobster Tails:

• Using kitchen shears, slice lengthwise down the top of each shell from the thick end toward the tail, stopping before the tail tip so it remains attached.
• Loosen the meat from inside the shell with your fingers, then gently lift and push the meat upward so it rests on top of the split shell; place the prepared tails on a baking tray.
• Stir the melted butter with salt, paprika, and black pepper in a small bowl. Brush this mixture evenly over the exposed lobster meat.
• Move an oven rack close to the broiler element and preheat the oven to broil (or use a steam/grill setting if available) so it is very hot before cooking.
• Broil the lobster tails until the flesh turns opaque and firms up—about 5 minutes for 4–6 ounce tails and up to 10 minutes for 10 ounce tails. Watch closely to avoid overcooking.
• Remove lobster from the oven and transfer to plates; serve with the lemon cream sauce spooned over or on the side.

Lemon Cream Sauce:

• Heat olive oil in a small saucepan over medium heat. Add minced garlic and cook, stirring, until it becomes very soft but does not brown—about 7 minutes.
• Pour in the vegetable broth, add lemon juice and heavy cream, then whisk to combine. Bring the mixture to a gentle simmer, then remove from the heat and keep warm until serving.