Heat the olive oil in a large Dutch oven or deep saucepan over medium heat. Add the diced onion, carrots, and celery, cooking for about 5 minutes until the vegetables soften.

Stir in the minced garlic and minced beef. Cook for 5-6 minutes, breaking the meat up with a wooden spoon, until browned completely. Drain away any excessive excess fat if desired.

Add the tomato puree and Italian seasoning to the pan, stirring well for 1 minute to coat the meat and toast the spices.

Pour in the canned chopped tomatoes and beef stock. Season lightly with salt and black pepper. Bring the entire mixture to a boil, then reduce the heat to low and simmer uncovered for 10 minutes.

Drop the broken lasagna sheets directly into the simmering soup. Cook for an additional 8-10 minutes, stirring occasionally to prevent the pasta from sticking together, until the noodles are al dente.

While the pasta cooks, mix together the ricotta, mozzarella, and parmesan cheeses in a small bowl until fully combined.

Ladle the hot lasagna soup into bowls, then dollop a generous spoonful of the mixed cheeses into the center of each serving. Serve immediately while hot.