Preheat the oven to 350°F (175°C). Spray a 9x13 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 less than 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. Mix until well combined.
Spoon the cheese mixture into each cooled shell and place the filled shells 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 dish with foil and bake for 25 minutes, or until the casserole is hot and bubbly. Remove foil for the last 5 minutes if you prefer a browned top.
Let rest briefly, then serve immediately.