Preheat grill to medium-high. In a large bowl, toss together shrimp, tomatoes, melted butter, garlic and Italian seasoning. Season with salt, pepper and a pinch of red pepper flakes.
Cut 6 large pieces of heavy-duty foil about 10 inches long. Divide shrimp mixture between foil pieces and pour 1 tablespoon cream over each packet. Top with about 1 tablespoon Parmesan cheese for each packet and fold foil crosswise to completely cover shrimp. Tightly fold up the ends to seal.
Place foil packets on the grill. Cook until shrimp is cooked through and the tomatoes just start to burst, about 10 minutes.
To serve, carefully unseal foil and top with additional Parmesan cheese and basil, if desired.