Preheat the oven to 350°F (175°C). Spray a 9×13-inch baking dish with cooking spray and spread half of the marinara sauce evenly on the bottom; set aside.
Bring a large pot of water to a boil and add 1 tablespoon kosher salt. Cook the jumbo pasta shells until about 3 minutes shy of al dente, following package directions.
Drain the shells in a colander and rinse with cool water to stop cooking; set aside to cool slightly.
In a large bowl, combine the whipped cottage cheese or ricotta, grated Parmesan, egg, minced garlic, minced parsley, chopped basil, 1/2 teaspoon salt, and 1/2 teaspoon fresh ground pepper. Stir until well mixed.
Spoon the cheese mixture into each cooked shell (use a spoon or small scoop) and place the filled shells seam-side up in the prepared baking dish, nestling them into the sauce.
Pour the remaining marinara sauce over the filled shells and sprinkle the grated mozzarella evenly on top.
Cover the baking dish with foil and bake for 25 minutes, until heated through and bubbly. Remove foil for the last few minutes if you want the cheese browned. Serve immediately.
