Preheat the oven to 400 degrees F. Pat the shrimp dry with paper towels.
Grease a large non-stick baking sheet with olive oil and spread them out in one layer.
Season them with salt and pepper. Top each shrimp with a scant tablespoon of sauce then about a tablespoon of mozzarella, going back over them if needed to use up all the cheese.
Sprinkle the Parmesan over them and then drizzle lightly with olive oil.
Bake 12 - 16 minutes, you can pull out one of the shrimp to test it and see if it's done.
Heat the broiler and with the oven door open broil for 1 - 3 minutes, keeping a close eye on them, until the tops are browned.
Sprinkle with parsley and serve with cooked pasta, rice or with crusty bread and a salad.