Heat the olive oil in a large Dutch oven or heavy pot over medium-high heat. Add the Italian sausage or lean ground beef and cook for 5–7 minutes, breaking it into small pieces, until browned; drain excess fat if needed.

Add the diced onion and cook for 3–4 minutes, until softened. Stir in the garlic, tomato paste, Italian seasoning, and optional red pepper flakes, then cook for 30–60 seconds.

Pour in the crushed tomatoes and broth, then season with kosher salt and black pepper. Scrape the browned bits from the bottom of the pot as the liquid comes to a boil.

Reduce the heat and simmer the tomato mixture for about 10 minutes. This gives the broth time to develop a deeper, more cohesive flavor before the noodles are added.

Stir in the broken lasagna noodles and simmer uncovered for 10–12 minutes, stirring occasionally, until the noodles are tender. Avoid cooking them too long because they continue absorbing broth as the soup stands.

Taste the soup and adjust the salt, pepper, and red pepper flakes. Ladle it into bowls and finish each serving with ricotta, mozzarella, Parmesan, and fresh basil or parsley.