Set Instant Pot to saute. Once hot, add ground beef. Cook, stirring, until browned and no longer pink.
Finely dice onion and mince garlic; add to Instant Pot and season with 1/4 teaspoon salt and 1/4 teaspoon pepper. Continue to cook until onion is translucent.
Peel and dice carrots; dice celery. Drain and rinse the beans. Add to Instant Pot along with all remaining ingredients, except the cheese.
Place cover on Instant Pot, seal the vent. Using the manual setting, set timer for 2 minutes. When the time is up, allow the pressure to naturally release for 5 minutes. Quick release remaining pressure; remove the top and stir.
Serve the soup topped with fresh Parmesan cheese.