Heat a large heavy-bottomed pot over medium heat and add a tablespoon of olive oil. Once shimmering, add diced onion and cook until translucent, about 5 minutes, until fragrant and soft.
Add minced garlic to the pot and cook for about 30 seconds, stirring constantly, until fragrant.
Add ground beef to the pot, breaking it apart with your wooden spoon. Cook until browned and cooked through, about 8 minutes, until the meat is no longer pink and releases some fat.
Pour in crushed tomatoes and beef broth, stirring to combine. Bring the mixture to a gentle simmer, about 10 minutes, allowing flavors to meld and the broth to thicken slightly.
Add broken lasagna noodles to the pot and cook until tender but still firm, about 10 minutes. Stir occasionally to prevent sticking.
Taste the soup and season with salt and pepper as needed. Adjust seasoning to your preference.
Sprinkle shredded mozzarella and chopped fresh basil over the soup. Cover and cook for about 2 minutes, until the cheese melts and basil releases its aroma.
Serve the hot lasagna soup in bowls, garnished with extra basil if desired, and enjoy the comforting flavors.