Begin by chopping the onion and mincing the garlic, setting them aside for later.
Heat the large heavy-bottomed pot over medium heat and add a splash of oil. Sauté the chopped onion and garlic until fragrant and translucent, about 2-3 minutes.
Add the ground beef to the pot, breaking it apart with a spoon. Cook until browned and cooked through, about 5-7 minutes, until the meat is no longer pink.
Pour in the crushed tomatoes and beef broth, stirring to combine everything well.
Bring the mixture to a gentle simmer and stir in red pepper flakes, salt, and pepper. Let it simmer uncovered for about 20 minutes, allowing flavors to meld and the broth to thicken slightly.
While the soup simmers, cook the broken lasagna noodles in a separate pot until just al dente, then drain and set aside.
Add the diced ricotta or shredded mozzarella cheese into the simmering soup, stirring gently to create a creamy, gooey texture.
Stir in the cooked pasta pieces into the soup, allowing them to soak up the flavorful broth and soften further.
Chop the fresh basil and sprinkle it into the soup just before serving, adding a bright, aromatic note.
Ladle the hot soup into bowls, garnish with additional cheese or basil if desired, and enjoy while steaming and hearty.