Brown the meat: Heat olive oil in a large pot over medium-high heat. Add the sausage and ground beef, breaking it up with a spoon. Cook until browned with no pink remaining, about 6–8 minutes.
Drain excess fat if needed.
Sauté aromatics: Add the diced onion to the pot. Cook until softened, 4–5 minutes. Stir in the garlic and cook for 30 seconds, just until fragrant.
Build flavor: Add tomato paste, oregano, basil, red pepper flakes, salt, and black pepper.
Cook the paste for 1–2 minutes to deepen the flavor, stirring to coat the meat.
Add liquids: Pour in the crushed tomatoes and chicken broth. Stir well and bring to a gentle boil. Reduce to a simmer and cook for 10 minutes to let the flavors meld.
Cook the noodles: Stir in the broken lasagna noodles.
Simmer, stirring occasionally to prevent sticking, until the noodles are al dente, about 10–12 minutes. Add 1 cup water if the soup gets too thick.
Adjust seasoning: Taste and add more salt, pepper, or a teaspoon of sugar if the tomatoes are very acidic.
Make the cheese mixture: In a small bowl, mix ricotta and Parmesan. This will be your creamy dollop for serving.
Add the mozzarella: Turn the heat to low and stir in the mozzarella until melty and stringy.
Keep the soup warm but do not boil.
Serve: Ladle the soup into bowls. Top each bowl with a generous spoonful of the ricotta-Parmesan mixture and a sprinkle of extra Parmesan and fresh basil or parsley.