In a large Dutch oven, heat oil over medium-high heat until shimmering. When the oil is hot, add the ground beef, onion and bell pepper. Cook until the meat is no longer pink and the vegetables are soft, about 7-10 minutes. Add the garlic and Italian seasoning; cook for 30 seconds. Drain off the fat.
Add the tomatoes, marinara sauce, broth, water, and sugar, using a wooden spoon to scrape up any browned bits from the bottom of the pot as you stir. Bring to a boil, then reduce the heat to low. Cover the pot with a lid; simmer the soup for 15 minutes.
Add the broken lasagna noodles to the pot. Simmer, uncovered, stirring occasionally, until the noodles are tender, about 7-10 minutes.
While the noodles cook, make the topping by stirring together the ricotta, Parmesan, and pesto in a small bowl. Taste and season with salt and pepper, if desired.
Ladle the soup into serving bowls. Add a dollop of the ricotta mixture to each bowl; garnish with fresh herbs. Alternatively, you can just sprinkle grated Parmesan on top of each bowl.