01 - Heat olive oil in a large heavy-bottomed pot or Dutch oven over medium heat. Add the diced onion, carrot, and zucchini (if using). Sauté for 4 to 5 minutes until the vegetables are softened and the onion is translucent.
02 - Add the minced garlic to the pot and cook for 1 minute, stirring constantly, until fragrant.
03 - Add the ground beef or Italian sausage to the pot. Season with salt and black pepper. Cook for 5 to 7 minutes, breaking the meat apart with a wooden spoon, until fully browned and no pink remains. Drain any excess fat if necessary.
04 - Stir in the tomato paste, crushed tomatoes, and diced tomatoes. Add the dried basil, oregano, thyme, and 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 the heat to medium-low. Let it simmer uncovered for 10 minutes to allow the flavors to meld together.
06 - Add the broken lasagna noodle pieces to the pot. Continue simmering for 12 to 15 minutes, stirring occasionally to prevent the pasta from sticking to the bottom, until the noodles are tender.
07 - Remove the pot from heat. Stir in half of the shredded mozzarella and half of the Parmesan until melted and incorporated. Taste and adjust seasoning with 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 fresh chopped basil or parsley. Serve immediately with crusty bread or garlic toast.