Heat oven with rack in middle position to 350 deg. Bring 4 qut. of water to boil in large pot. Stir in 1 Tbsp salt and pasta, cook stirring occasionally , until pasta begins to soften but is not cooked through, 5-7 min. When cooked drain and leave in colander.
Whisk cottage cheese, eggs, and 1 cup Parmesan cheese together in medium bowl.
In 12” skillet heat oil and garlic and cook until fragrant but not brown, about 2 min. Stir in tomato sauce, diced tomatoes, and oregano. Simmer until thickened, about 10 min. Remove from heat and stir in basil and sugar and season with salt and pepper.
Stir cornstarch into heavy cream in small bowl. Add to empty large pot, bring to simmer, cook until thickened, 3-4 min.
Remove pot from heat and add cottage cheese mixture, 1 cup tomato sauce, half of mozzarella and stir to combine. Add pasta and stir to coat thoroughly with sauce.
Transfer pasta to 9×13 baking dish and spread remaining sauce on top, sprinkle remaining Parmesan and mozzarella on top. Cover tightly with foil and bake for 30 min. Remove foil and cook until cheese is bubbling and beginning to brown, about 30 min. longer. Cool for 20 min. prior to serving