Heat olive oil in a large Dutch oven over medium-high. Add beef, onion, and carrot. Cook for 6 to 8 minutes, breaking up the meat, until browned and the vegetables soften. Drain excess fat if needed.

Stir in garlic, Italian seasoning, fennel seed, and red pepper flakes. Cook for 1 minute. Add tomato paste and cook for another minute.

Stir in crushed tomatoes, marinara, beef broth, salt, and black pepper. Scrape the bottom of the pot and bring to a gentle boil.

Add broken lasagna noodles. Simmer uncovered for 10 to 12 minutes, or according to package timing, stirring frequently until just al dente. Add more broth if the soup becomes too thick.

Stir in spinach and cook for 1 to 2 minutes, until wilted. Taste and adjust salt, pepper, and broth.

Mix ricotta with half the Parmesan and half the herbs. Ladle soup into bowls and top with ricotta mixture, mozzarella, remaining Parmesan, and herbs.