In a large Dutch oven or heavy-bottomed pot, brown the ground beef and Italian sausage over medium-high heat, breaking the meat into small crumbles. Once browned, use a slotted spoon to transfer the meat to a plate, leaving about 2 tablespoons of drippings in the pot.

Reduce the heat to medium. Add the diced onion and cook until softened, about 5 minutes. Add the minced garlic and red pepper flakes (if using) and cook for 30 seconds until fragrant. Stir in the tomato paste and cook for 1 minute, stirring constantly.

Return the browned meat to the pot. Pour in the crushed tomatoes and tomato sauce. Add the sugar, 1 teaspoon of salt, and 1/2 teaspoon of black pepper. Stir together and bring to a gentle simmer. Reduce heat to low, partially cover, and let simmer for 20-25 minutes, stirring occasionally. In the last 5 minutes, stir in the heavy cream. Taste and adjust seasoning. Set aside.

While the sauce simmers, make the cheese filling. In a large bowl, combine the ricotta cheese, softened cream cheese, cottage cheese, eggs, chopped parsley, dried oregano, 1/2 cup of the grated Parmesan cheese, and a generous pinch of salt and pepper. Use a spatula or hand mixer to combine until perfectly smooth and creamy.

Preheat your oven to 375°F (190°C). Spread a thin layer of the meat sauce (about 1 cup) on the bottom of a 9x13-inch baking dish.

Lay down a single layer of no-boil lasagna noodles, breaking them to fit if necessary. Spread 1/3 of the creamy cheese mixture over the noodles. Sprinkle with 1 cup of shredded mozzarella cheese. Spoon 1/3 of the remaining meat sauce over the mozzarella. Repeat these layers two more times: noodles, cheese mixture, mozzarella, meat sauce.

For the final top layer, lay down the last of the noodles. Spread any remaining meat sauce over them. Sprinkle the rest of the mozzarella cheese and the remaining 1/2 cup of grated Parmesan cheese over the top.

Cover the baking dish tightly with aluminum foil. Bake for 40 minutes.

After 40 minutes, carefully remove the foil. Increase the oven temperature to 400°F (200°C) and bake for an additional 10-15 minutes, or until the top is golden brown and the sauce is bubbling. For an extra-crispy top, broil for the final 1-2 minutes, watching closely.

Remove the lasagna from the oven and let it rest on a wire rack for at least 20-25 minutes before slicing and serving.