01 - Heat olive oil in a large heavy-bottomed pot or Dutch oven over medium heat. Add diced onion, carrot, and zucchini (if using); sauté for 4 to 5 minutes until the vegetables are softened and translucent.
02 - Add minced garlic and cook for 1 minute, stirring constantly, until fragrant and lightly golden.
03 - Add ground beef or Italian sausage to the pot, season generously with salt and black pepper, and cook for 5 to 7 minutes, breaking the meat apart with a wooden spoon until fully browned and no pink remains. Drain excess fat if necessary.
04 - Stir in tomato paste, crushed tomatoes, and diced tomatoes. Add dried basil, oregano, thyme, and crushed red pepper flakes if using. Pour in the broth and stir well to combine all ingredients.
05 - Bring the soup to a gentle boil, then reduce heat to medium-low and let it simmer uncovered for 10 minutes to allow the flavors to meld together.
06 - Add the broken lasagna noodle pieces to the pot. Simmer for 12 to 15 minutes, stirring occasionally to prevent sticking, until the pasta is tender and cooked through.
07 - Stir in half of the shredded mozzarella and half of the Parmesan cheese until melted and evenly distributed. Taste and adjust seasoning with additional salt and pepper as needed.
08 - Ladle the hot soup into serving bowls. Top each portion with generous dollops of ricotta cheese, a sprinkle of the remaining mozzarella and Parmesan, and freshly chopped basil or parsley. Serve immediately while hot.