Turn Instant Pot to sauté; heat for 1 minute.

Add a small amount of olive oil (1 tablespoon max) and the ground turkey; cook, stirring occasionally, until browned, about 5 minutes.

Stir in mushrooms, onion, bell pepper, and garlic.

Stir in broth (or 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, and release steam until it stops.

Carefully uncover; set to sauté.

Bring mixture to a boil; add penne pasta, and cook, stirring often, until tender, about 11 minutes. (If you use lasagna noodles, the time will be less ~ 9 minutes.)

Turn off Instant Pot; stir in half-and-half.

Ladle soup into bowls and top with shredded mozzarella.