Start by prepping your lobster tails. Using sharp kitchen scissors or a knife, cut down the top of the shell lengthwise, stopping just before the tail fin. Gently pull the lobster meat out from the shell, keeping it attached at the base, and rest it on top of the shell.
In a small bowl, combine the unsalted butter, minced garlic, and freshly squeezed lemon juice. Add a pinch of salt and pepper to taste. Stir well to create a smooth garlic butter sauce.
Heat a large skillet over medium heat. Place the lobster tails meat-side down and cook for about 2-3 minutes until it starts to turn opaque. Flip the tails, then generously brush the garlic butter sauce all over the lobster meat. Continue cooking for another 3-4 minutes, basting occasionally with the butter sauce, until the lobster is fully cooked and tender.
While the lobster cooks, rinse the long-grain rice under cold water until the water runs clear. In a medium saucepan, bring the chicken broth to a boil. Add the rice, reduce heat to low, cover, and simmer for 15 minutes or until the rice is tender and liquid is absorbed.
Once cooked, remove the saucepan from heat. Stir in the grated Parmesan cheese and chopped fresh parsley. Season with salt and pepper to taste.
Serve each lobster tail atop a bed of Parmesan rice. Spoon any remaining garlic butter from the skillet over the lobster for extra richness. Garnish with additional parsley or a lemon wedge if desired.