Set the Instant Pot to sauté mode and add olive oil. Once hot, add onions and garlic and sauté until softened, about 2 minutes.
Add diced carrots, and celery to the pot and sauté for another 4 minutes until slightly softened.
Stir in the zucchini, basil, oregano, thyme, vegetable broth, diced tomatoes, and kidney beans. Add the ditalini pasta. Close the lid, set the valve to sealing, and cook on manual high pressure for 4 minutes.
Once cooking is complete, do a quick release. Open the lid safely, and stir in the baby spinach until wilted. Season with salt and pepper to taste. Garnish with grated Parmesan cheese and serve hot.