Set Instant Pot to sauté mode and heat olive oil. Add Italian sausage and cook, breaking it up with a spoon, until browned (about 5 minutes).
Add onion, carrots, and celery. Cook for 3-4 minutes until vegetables start to soften.
Stir in garlic, oregano, basil, and red pepper flakes. Cook for 1 minute until fragrant.
Add white beans, chicken broth, and diced tomatoes with their juice. Stir to combine and scrape up any browned bits from the bottom.
Close the lid, set valve to sealing, and cook on high pressure for 10 minutes.
Quick release the pressure, then open the lid carefully. Set to sauté mode again.
Stir in the fresh spinach or kale and let it wilt for 2-3 minutes. Season with salt and pepper to taste. Serve hot with a generous sprinkle of Parmesan cheese on top.