Step 1: Preheat your oven to 375°F (190°C). Line a baking sheet with parchment paper for easy cleanup.
Step 2: Pat the snapper fillets thoroughly dry with paper towels. Drizzle them with olive oil, then season generously with salt and freshly ground black pepper on both sides. If desired, place a few thin lemon slices on top of each fillet.
Step 3: Bake the seasoned snapper for 15-20 minutes, or until the fish flakes easily with a fork and reaches an internal temperature of 145°F (63°C). Be careful not to overcook.
Step 4: While the snapper bakes, prepare the lobster cream sauce. In a small saucepan, melt 1 tablespoon of unsalted butter over medium heat. Add the finely minced shallots and sauté for 2-3 minutes until they soften. Stir in the minced garlic and cook for another minute until fragrant.
Step 5: Pour in 1/4 cup of dry white wine. Bring it to a simmer and let it reduce by half, which should take about 3-5 minutes, scraping up any browned bits from the bottom of the pan.
Step 6: Stir in 1 cup of heavy cream and bring the mixture to a gentle simmer. Cook, stirring occasionally, for 5-7 minutes, allowing the sauce to reduce and thicken slightly.
Step 7: Gently fold in 4 ounces of roughly chopped cooked lobster meat and 2 tablespoons of grated Parmesan cheese. Season the sauce with salt and pepper to taste. Continue to simmer gently for 2-3 minutes to heat the lobster through and allow the flavors to meld. Finally, stir in 2 tablespoons of fresh chopped parsley.
Step 8: Carefully transfer the baked snapper fillets to individual serving plates. Spoon a generous amount of the warm, rich lobster cream sauce over each fillet. Garnish with additional fresh parsley and serve immediately.