Set the Instant Pot to sauté mode. Add the olive oil, onion, garlic, and celery and sauté for about 3 minutes, stirring, until the onions are translucent and the celery has softened.
Add the tomato paste, basil, oregano, thyme, diced tomatoes, broth, zucchini, green beans, and pasta. Stir to combine all the ingredients.
Cook:
Close the lid and seal the valve. Set to manual high pressure (HP) for 6 minutes. It takes about 8 minutes for the Instant Pot to reach high pressure, then it will cook for 6 minutes.
When the timer goes off, release the pressure by opening the valve. Remove the lid, add the white beans, and stir to combine. Put the lid on and let the soup sit for 2 minutes to warm up the beans.
Serve:
Ladle the minestrone into bowls and sprinkle Parmesan cheese on top.
Storage:
Once cooled, cover the pot with a silicone lid or transfer leftovers into an airtight container and refrigerate for up to 4 days.