Heat the olive oil in a large pot over medium-high heat. Add the sausage, breaking it into small pieces as it cooks, for 5-7 minutes until browned and cooked through. Remove the sausage with a slotted spoon and set aside on a paper towel-lined plate.
In the same pot with the rendered sausage fat, add the diced red bell pepper, sweet onion, and carrots. Sauté for 3-4 minutes until they begin to soften. Add the minced garlic in the final minute and stir constantly.
Stir in the oregano, basil, thyme, red pepper flakes, salt, and black pepper. Return the cooked sausage to the pot and stir to combine.
Pour in the marinara sauce and chicken broth, stirring to combine. Add the parmesan rind to the pot and bring the soup to a simmer.
Break the lasagna sheets into 1-inch pieces and add them to the simmering broth. Simmer for 14-15 minutes, until the pasta is tender.
Reduce heat to low and stir in the cream and mozzarella, allowing the cheese to fully melt for about 1-2 minutes.
Ladle the hot soup into bowls and top each serving with a dollop of ricotta, a spoonful of basil pesto, freshly grated parmesan, and torn fresh basil.