Turn Instant Pot to sauté; heat for 1 minute. Add beef; cook, stirring occasionally, until browned, about 5 minutes. Stir in mushrooms, onion, bell pepper, and garlic. Stir in stock, tomatoes, tomato paste, oregano, salt, and black pepper. Cover with lid; turn to manual. Turn lid valve to seal, and set to high pressure for 10 minutes.
Release valve with a towel (be careful of the pressurized steam), and release steam until it stops. Carefully uncover; set to sauté. Bring mixture to a boil; add lasagna noodles, and cook, stirring often, until tender, about 9 minutes. Turn off Instant Pot; stir in half-and-half. Divide soup evenly among 8 bowls. Top evenly with mozzarella and basil.