Adjust oven rack to middle position and heat oven to 350 degrees. Whisk cottage cheese, eggs, and 1 cup Parmesan together in medium bowl; set aside. Bring 4 quarts of water to boil in large Dutch oven over high heat. Stir in 1 tablespoon salt and pasta; cook, stirring occasionally, until pasta begins to soften but is not yet cooked through, 5 to 7 minutes. Drain pasta and leave in colander (do not wash Dutch oven).
Meanwhile, brown ground hamburger with diced onion, set aside. 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, oregano; and browned hamburger, simmer until thickened, about 10 minutes. Off heat, stir in 1/2 cup basil and sugar, then season with salt and pepper.
Stir cornstarch into heavy cream in small bowl; transfer mixture to 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 of your tomato sauce mixture, and 3/4 cup mozzarella, then stir to combine. Add pasta and stir to coat thoroughly with sauce.
Transfer pasta mixture to a prepared 13- by 9-inch baking dish and spread remaining tomato sauce evenly over pasta. Sprinkle remaining 3/4 cup mozzarella and remaining 1/2 cup Parmesan over 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.
NOTE: If you don't have heavy cream, whole milk can be substituted by increasing the amount of cornstarch to 2 teaspoons and increasing the cooking time in step 3 by 1 to 2 minutes. Avoid preshredded mozzarella cheese, as it does not melt well.