Heat a large Dutch oven over medium-high heat. Add the ground beef and cook for 6 to 8 minutes, breaking it into small pieces, until no pink remains.
Reduce the heat to medium. Add the diced onion and cook for about 4 minutes. Stir in the garlic and cook for another 30 seconds.
Add the tomato paste, Italian seasoning, and red pepper flakes. Cook for 1 to 2 minutes, stirring until the tomato paste becomes darker.
Pour in the crushed tomatoes, diced tomatoes, and 5 cups beef broth. Add the salt and black pepper. Scrape the bottom of the pot and bring the mixture to a gentle simmer.
Break the lasagna sheets into rough 1½- to 2-inch pieces.
Add the broken noodles to the soup. Simmer for 10 to 12 minutes, stirring every 2 to 3 minutes, until the pasta is tender. Add up to ½ cup extra broth if the soup becomes too thick.
Combine the ricotta with ¼ cup Parmesan in a bowl. Stir until smooth.
Lower the heat and stir the remaining ¼ cup Parmesan into the soup for about 30 seconds.
Turn off the heat and let the soup sit uncovered for 5 minutes. Add ¼ to ½ cup warm broth if you want a thinner consistency.
Ladle into bowls. Top each serving with the ricotta mixture, shredded mozzarella, and fresh basil or parsley. Let the cheese soften for about 1 minute before serving.
