-
Place a large, heat-proof, skillet on the grill to preheat (directly over the heat).
-
Add the reserved lobster shells, half & half, onion, celery, basil, and crushed red pepper flakes to the skillet. Bring to a simmer, stirring occasionally.
-
Once simmering, cover, and transfer to the side of the grill not directly over the heat. Heat for 20-30 minutes, or until slightly reduced, and strain. Discard the shells and return the strained, flavored cream to the skillet.
-
Place the skillet directly over the heat, add parmesan and tomato paste, and whisk to combine.
-
Bring to a simmer and cook, whisking frequently, until the sauce has thickened, about 2 minutes.
-
Season to taste with salt and pepper, transfer the skillet to the side of the grill not directly over the heat, and stir in the lobster meat.
-
Let the lobster sit in the sauce, just enough to reheat, before adding the pasta and tossing to coat. If the sauce is starting to become too thick, add a little of the reserved pasta water to thin.
-
Transfer the pasta to a serving platter and garnish with basil, pepper, and parmesan.