Bring a large pot of lightly salted water to a boil. Add pasta and cook for only 3-4 minutes and then drain. You want to start the cooking process, but you need them firm enough to stuff. They will continue cooking in the oven.
In a large bowl, mix eggs, ricotta, mascarpone, half the mozzarella, half the Parmesan, Italian seasoning, basil, garlic, salt and red pepper flakes until well combined. Stuff cooked shells with ricotta mixture by piping through a resealable plastic bag with the corner snipped off. Place stuffed shells in a 9x13 inch baking dish.
Cover shells with pasta sauce and then top with remaining shredded cheese. Cover with foil.
Bake in preheated oven 45 minutes. Remove foil and continue cooking for another 5-15 minutes until edges are bubbly and cheese is melted.