Set the Instant Pot to saute mode. Add the italian sausage and break it into crumbles as it cooks, about 5 to 6 minutes until browned through. Drain any excess grease if needed.
Add the diced onion and saute for 3 minutes. Stir in the minced garlic and tomato paste, cooking for 1 minute until fragrant.
Pour in the crushed tomatoes, diced tomatoes, and chicken broth. Add the italian seasoning, salt, and red pepper flakes. Stir well. Break the lasagna noodles into rough 2-inch pieces and push them into the liquid, making sure they are submerged.
Lock the lid, set the valve to sealing, and cook on high pressure for 4 minutes. Quick release the pressure as soon as the cook time is done.
While the soup cooks, stir together the ricotta cheese with a pinch of salt and a crack of black pepper in a small bowl.
Open the lid and give the soup a good stir. The noodles will continue to absorb liquid as they sit, so do not worry if it seems a bit thin at first. Taste and adjust the seasoning.
Ladle the soup into bowls. Top each bowl with a generous dollop of seasoned ricotta, a handful of shredded mozzarella, fresh basil, and grated parmesan cheese. The heat from the soup will melt the cheeses beautifully.