Cook the noodles according to package directions. Drain and rinse; set aside.
Spray a large nonstick skillet with nonstick spray and set over medium-high heat. Add the squash and cook until golden, 2-3 minutes per side. Set aside.
Combine the cottage cheese, spinach, 2 cups of the mozzarella, 1/4 cup of the Parmesan, the eggs, basil, garlic and salt.
Preheat the oven to 375°F Spread 1 cup sauce in a 9x13 inch baking dish. Top with 3 noodles, 2 cups filling, and the squash. Top with 3 noodles, 1 cup sauce and remaining filling. Top with remaining noodles, sauce and cheeses. Cover and bake 30 minutes.
Uncover. Bake 20 minutes. Let stand 10 minutes before serving.