Brown the ground beef: Heat olive oil in a large pot or Dutch oven over medium-high heat. Add the ground beef and cook, breaking it apart with a spoon, until no pink remains, about 6 minutes. Drain excess fat.

Add garlic and tomato paste: Stir in the minced garlic, tomato paste, and Italian seasoning. Cook for about 1 minute until fragrant and the paste darkens slightly.

Pour in tomatoes and broth: Add the crushed tomatoes, beef broth, soy sauce, and rice vinegar. Scrape up any browned bits from the bottom of the pot with a wooden spoon.

Bring to a boil: Increase heat to bring the mixture to a gentle boil, then reduce to a simmer. Let it cook uncovered for 10 minutes so the flavors deepen.

Add the broken noodles: Stir in the broken lasagna noodles. Cook for about 10 minutes, stirring occasionally so they don't stick, until just tender.

Season to taste: Taste the soup and add salt and black pepper as needed. Remember the cheeses added next bring their own saltiness.

Stir in mozzarella: Add the shredded mozzarella to the pot and stir until melted and incorporated into the broth.

Top with ricotta: Ladle the soup into bowls and spoon a dollop of ricotta cheese on top of each serving, letting it soften into the hot broth.

Garnish and serve: Sprinkle with grated Parmesan and fresh basil if desired. Serve immediately while hot.