Heat the olive oil in a large pot over medium-high heat. Add the ground beef and Italian sausage. Cook, breaking up the meat, until browned, about 8 minutes.
Add the onion and cook until softened, about 5 minutes. Stir in the garlic and cook for 1 more minute until fragrant.
Stir in the crushed tomatoes, tomato paste, and chicken broth. Add Italian seasoning, basil, oregano, and red pepper flakes. Bring to a boil, reduce heat, and simmer for 15 minutes.
Add the broken lasagna noodles and cook for 10–12 minutes, or until tender.
Stir in the spinach until wilted, about 2 minutes. If using, stir in heavy cream. Season with salt and pepper to taste.
In a mixing bowl, combine ricotta, half of the mozzarella, half of the Parmesan, parsley, and basil.
Ladle soup into bowls. Top each with a scoop of the cheese mixture and sprinkle with remaining mozzarella and Parmesan. Serve warm.