1. Bring a large pot of salted water to a boil. Add the lasagna noodles and cook according to the package’s instructions. Drain and reserve.
2. In a large pot, heat the olive oil over medium heat. Add the onion, celery and carrot, and sauté until the vegetables are tender, 6 to 7 minutes. Add the garlic and sauté until fragrant, about 1 minute more.
3. Add the meat to the pan and use your spoon to break it up into small pieces. Sauté until browned, 4 to 5 minutes.
4. Stir in the oregano, thyme and tomatoes. Add the broth and bring the mixture to a simmer over medium-low heat.
5. Cover the pot and simmer 25 to 30 minutes.
6. While the soup simmers, slice each lasagna noodle into ⅓-inch pieces (slice from the shorter side so that each piece has frilly ends on both sides).
7. When the soup has finished simmering, stir in the noodles, spinach and Parmesan. Season with salt and pepper to taste.
8. In a small bowl, stir the ricotta with the mozzarella. To serve the soup, scoop 2 tablespoons of the cheese mixture into the base of each bowl, then ladle soup on top. Serve immediately, garnished with basil.