Adjust oven rack to middle position and heat oven to 350°F. Whisk cottage cheese, eggs, and 1 cup Parmesan together in a medium bowl; set aside.
Bring 4 quarts of water to boil in a large Dutch oven over high heat. Stir in 1 tablespoon salt and pasta; cook for 5-7 minutes, stirring occasionally until pasta begins to soften but is not yet cooked through. Drain pasta and leave it in a colander (do not wash Dutch oven).
Meanwhile, heat oil and garlic in 12-inch skillet over medium heat until garlic is fragrant but not brown, about 2 minutes.
Stir in tomato sauce, diced tomatoes, and oregano; simmer until thickened, about 10 minutes. Off heat, stir in ½ cup basil and sugar, then season with salt and pepper.
Stir cornstarch into heavy cream in a small bowl; transfer mixture to the now-empty Dutch oven set over medium heat.
Bring to simmer and cook until thickened, 3 to 4 minutes. Remove pot from heat and add cottage cheese mixture, 1 cup tomato sauce, and ¾ cup mozzarella, then stir to combine.
Add pasta and stir to coat thoroughly with sauce.
Transfer pasta mixture to 13- by 9-inch baking dish and spread remaining tomato sauce evenly over pasta. Sprinkle remaining ¾ cup mozzarella and remaining 1/2 cup Parmesan over the top.
Cover baking dish tightly with foil and bake for 30 minutes. Remove foil and continue to cook until cheese is bubbling and beginning to brown, about 30 minutes longer. Cool for 20 minutes. Sprinkle with a little fresh basil, serve, and enjoy!
We highly recommend doubling this recipe! Double wrap your leftovers in foil, label, and freeze for up to 6 months. When you're ready to serve, just thaw overnight in the refrigerator and then bake in the oven per recipe instructions.