Preheat oven to 375. To make filling, combine ricotta, 1 cup of the asiago cheese, crabmeat, parsley, onion and basil. Season to taste with salt and white pepper.
Pour 2 cups of the tomato sauce into a shallow casserole. Divide the filling evenly among the cooked shells and place them in the sauce. Spoon remaining sauce over shells.
Cover with foil and bake for 25 minutes. Remove and top with remaining asiago cheese and return to oven for 5 minutes.
