Cut down the center of each lobster shell lengthwise using kitchen shears and gently pull the meat upward to rest on top while keeping it attached at the base.
Brush the lobster meat with olive oil and season with salt, pepper, and smoked paprika if using.
Preheat the grill to medium-high heat (about 400°F). Place the lobster tails flesh-side up on the grill.
Grill the lobster tails for 6 to 8 minutes until the meat is opaque, lightly charred at the edges, and reaches an internal temperature of 140–145°F.
In a small saucepan, melt butter over medium heat, and sauté minced garlic for 30 to 60 seconds until fragrant.
Stir in heavy cream and simmer gently for 2 to 3 minutes.
Add grated Parmesan cheese, lemon juice, lemon zest, and red pepper flakes; simmer until slightly thickened.
Remove from heat, then stir in chopped fresh parsley.
Spoon the warm creamy garlic butter sauce generously over each grilled lobster tail and garnish with extra parsley and a squeeze of fresh lemon.
Serve immediately while hot and glossy.