Cook the Shells: Boil pasta shells until just al dente. Drain and rinse with cool water to stop cooking. Set aside.
Make the Vodka Sauce: In a large pan, heat olive oil over medium heat. Add garlic and red pepper flakes; cook 1 minute. Stir in vodka and let simmer for 2–3 minutes to reduce. Add crushed tomatoes, season with salt and pepper, and simmer for 10–15 minutes. Stir in heavy cream and Parmesan (if using). Simmer another 5 minutes and set aside.
Make the Filling: In a bowl, combine ricotta, mozzarella, Parmesan, egg, basil, salt, and pepper. Mix until smooth.
Stuff the Shells: Preheat oven to 375°F (190°C). Spread a thin layer of vodka sauce on the bottom of a baking dish. Fill each shell with about 1–2 tablespoons of the cheese mixture and place in the dish.
Assemble and Bake: Pour the remaining vodka sauce over the shells. Top with extra mozzarella or Parmesan if desired. Cover with foil and bake for 20 minutes, then uncover and bake 10 more minutes until bubbly and golden.