Heat olive oil in a large Dutch oven or heavy-bottomed pot over medium-high heat. Add ground beef (or sausage) and cook, breaking it up with a spoon, until browned. Drain any excess fat.

Add chopped onion to the pot and cook until softened, about 5-7 minutes. Stir in minced garlic, dried oregano, dried basil, and red pepper flakes (if using). Cook for another minute until fragrant.

Pour in the crushed tomatoes, tomato sauce, beef broth, granulated sugar (if using), salt, and black pepper. Stir well to combine. Bring the mixture to a gentle simmer.

Once simmering, add the broken lasagna noodle pieces to the pot. Stir gently to ensure they are submerged in the liquid. Reduce heat to medium-low, cover, and simmer for 15-20 minutes, or until the lasagna noodles are tender. Stir occasionally to prevent noodles from sticking.

While the soup simmers, prepare the ricotta swirl (if using). In a small bowl, combine ricotta cheese, grated Parmesan cheese, chopped fresh parsley, garlic powder, a pinch of salt, and a pinch of black pepper. Mix until well combined and creamy. Set aside.

Once the noodles are tender, taste the soup and adjust seasonings if necessary.

Ladle the hot lasagna soup into bowls. Dollop each serving with a spoonful of the ricotta mixture. Sprinkle with shredded mozzarella cheese and allow it to melt slightly from the heat of the soup. Garnish with torn fresh basil leaves and extra grated Parmesan cheese, if desired. Serve immediately.