Place an oven rack in the center position and preheat the oven to 375°F (190°C). Fill a large stockpot with 4 quarts (4 liters) of water, add 1 tablespoon of kosher salt, and bring to a full rolling boil. Set a colander in the sink.
Add 28 jumbo shells to the boiling water and stir gently right away. Cook for 2 minutes less than the package directs, usually about 9 to 10 minutes, stirring once or twice. Pour into the colander, rinse under cool running water, toss with 1 tablespoon olive oil, and spread on a baking sheet in a single layer.
Drain any pooled liquid from the ricotta. In a large mixing bowl, combine the drained ricotta, 1 1/2 cups shredded mozzarella, 1/2 cup grated Parmesan, egg, minced garlic, 1 tablespoon chopped parsley, Italian seasoning, 1/2 teaspoon salt, and 1/4 teaspoon black pepper. Stir in crushed red pepper flakes if desired. Mix until evenly combined, thick, and slightly stiff; do not overmix.
Spread 1 cup (240 ml) of marinara sauce across the bottom of the 9x13-inch baking dish. Tilt the dish to cover the corners so the shells do not stick.
Pick out the 24 best-shaped shells and set the four most torn ones aside as spares. Transfer the filling to a piping bag or zip-top bag and snip off a corner about 3/4 inch (2 cm) wide. Pipe about 2 tablespoons of filling into each shell so it mounds slightly above the rim. Set each filled shell in the sauce with the open side facing up, lining them up in a snug single layer.
Spoon the remaining 2 cups (480 ml) of marinara sauce over and around the shells. Sprinkle 1 1/2 cups (170 g) shredded mozzarella evenly across the top, then add 1/4 cup (25 g) grated Parmesan over the mozzarella. Cover the dish loosely with foil, tenting it so the foil does not touch the cheese.
Slide the dish into the oven and bake covered for 20 minutes. Remove the foil carefully, since hot steam will escape. Return the dish to the oven and bake uncovered for 10 to 15 minutes, until the sauce bubbles at the edges and the cheese has golden spots.
Let the dish rest for 5 minutes so the sauce thickens slightly and the shells hold together when lifted. Sprinkle the remaining 1 tablespoon of chopped parsley over the top. Serve 4 shells per person with extra sauce from the pan spooned over each portion.