Preheat the oven to 350°F (175°C).
Bring a large pot of water to a rapid boil and add 1 tablespoon kosher salt.
Add 16 ounces rotini and cook until about 1–2 minutes shy of the package al dente time, stirring occasionally.
Reserve 1/2 cup of the pasta cooking liquid, then drain the pasta in a colander.
In a large mixing bowl, combine drained rotini with 28 ounces spaghetti sauce (or marinara), 1/2 cup reserved cooking liquid, 16 ounces cottage cheese, and 1 cup shredded mozzarella; stir to combine and let cool slightly.
Stir the whisked large egg into the pasta mixture until evenly incorporated.
Transfer the mixture to a greased 9x13-inch (or 3-quart) baking dish and evenly sprinkle the remaining 1 cup shredded mozzarella over the top.
Bake for 30 minutes, or until the cheese is bubbly and the casserole is heated through.