Preheat oven to 450.
Salt a pan of water, add jumbo shells and boil for 12-15 minutes (want them uncooked in the center)
Combine the ricotta, 1/2 of the diced mozzarella, couple handfuls of the parmingiano, and half of the asiago, add the parsley.
Place the oil in the fry pan, cook the garlic and onions for 5 minutes.
Add tomatoes and season with salt and pepper. Simmer for 5 minutes.
Stir in basil.
Pour sauce into the dish.
Fill shells with rounded spoonfuls of the cheese mixture and arrange them with the seam down.
Top with sauce and remaining mozzarella and asiago.
Cook 6-8 minutes.