1. Preheat your grill to medium-high heat or set your oven to the broiling function. Complete all prep work before beginning.
2. Rinse the split lobster tails under cold water, pat them dry with paper towels, and season lightly with salt and pepper.
3. In a medium bowl, mix the melted unsalted butter with fresh lemon juice. Stir in minced garlic, smoked paprika, red pepper flakes, and finely chopped parsley and chives to create the cowboy butter sauce.
4. Generously coat each lobster tail with the prepared cowboy butter sauce, ensuring every crevice is covered for optimal flavor. Reserve some of the sauce for basting later.
5. Place the butter-coated lobster tails onto the grill with the flesh side down. Grill for approximately 5-6 minutes to achieve a subtle char while locking in moisture.
6. Flip the lobster tails onto their shell side and brush with the reserved cowboy butter sauce. Continue grilling for another 3-4 minutes until the meat becomes opaque and reaches an internal temperature of 140°F (60°C).
7. Remove the lobster tails from heat and let them rest for a few minutes before serving. This step helps the juices redistribute, making the lobster meat juicier.
8. Garnish the cooked lobster tails with additional fresh herbs and serve with lemon wedges on the side for extra citrus flavor. Consider pairing the dish with complementary sides such as garlic parmesan chicken pasta for a complete gourmet meal.