Add olive oil to a large Dutch oven and set over medium heat. Once the olive oil is shimmering, add the onions, carrots, and celery and cook 7–9 minutes or until the vegetables are soft and the onions are translucent.
Add the garlic, Italian seasoning, salt, pepper, and crushed red pepper. Cook for 1–2 minutes, or until the garlic is very fragrant.
Add the ground beef, breaking it up with a spatula, and cook for about 5 minutes, or until no longer pink. Add the tomato paste, stirring to incorporate it into the meat and vegetables, and cook for 2 minutes.
Add the diced tomatoes, marinara sauce, and vegetable broth and bring to a boil. Reduce heat to a simmer and cook for 15–20 minutes, or until the vegetables are very soft.
Once the vegetables are soft, return the soup to a boil and add the broken lasagna noodles. Cook at a gentle boil for 8 to 10 minutes, or until the pasta is al dente.
Serve the soup in large bowls topped with ricotta, grated Parmesan, and fresh basil.