Heat oven to 350°F. Brown sausage; drain on paper towel and set aside. Whisk cottage cheese, eggs, and 1 cup Parmesan together in medium bowl; set aside. Bring 4 quarts of water to boil in large pot over high heat. Stir in 2 tsp. 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 (leave pot unwashed).
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 small bowl; transfer mixture to now-empty pasta pot and bring to a simmer. 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 sausage; stir to coat well.
Transfer pasta mixture to 13x9-inch baking dish and spread remaining tomato sauce evenly over pasta. Sprinkle remaining ¾ 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. Cool for 20 minutes and serve.
Notes
Whole milk can be substituted by increasing the amount of cornstarch to 2 teaspoons and increasing the cooking time to thicken by 1 to 2 minutes.