Heat olive oil in a large heavy-bottomed pot over medium heat until shimmering. Add diced onion and cook, stirring occasionally, until translucent and fragrant, about 3-5 minutes. The onions should be soft and fragrant, with a slight sizzle.
Add minced garlic and cook for another 30 seconds, stirring constantly until garlic is fragrant and just starting to turn golden, filling the air with a warm aroma.
Push the vegetables to one side of the pot, then add ground beef or sausage, breaking it apart with your wooden spoon. Cook until browned and cooked through, about 8 minutes. The meat should be evenly browned and no pink remains.
Stir in crushed tomatoes and broth, bringing the mixture to a gentle simmer. The soup will start to bubble around the edges, releasing a rich, tomatoey aroma.
Add broken lasagna noodles to the simmering broth, stirring to ensure they are submerged. Continue cooking, stirring occasionally, until noodles are tender and cooked through, about 10 minutes. The broth should thicken slightly and become vibrant red with a rich aroma.
Stir in shredded mozzarella and grated Parmesan cheese, allowing them to melt smoothly into the soup. The cheese should create a gooey, creamy texture, and the broth will turn a richer, more inviting hue.
Season the soup with salt, pepper, and chopped basil, tasting and adjusting the seasonings as needed. The aroma should be bright and savory, with the basil adding a fresh note.
Serve hot, ladling the soup into bowls and garnishing with extra basil and cheese if desired. The finished dish should be bubbling and thick with tender noodles, cheesy goodness, and a vibrant tomato base.
