Turn the Instant Pot to sauté mode. Melt butter, then add onion, garlic, carrots, and celery. Cook until softened.
Add the potatoes, chicken, broth, thyme, salt, and pepper. Stir well.
Close the lid and cook on high pressure for 10 minutes. Let the pressure release naturally for 5 minutes, then quick release the rest.
Switch back to sauté mode. In a small bowl, whisk flour with cream until smooth. Stir into the pot and let simmer until the soup thickens.
Stir in peas and corn. Cook for 2 more minutes, then taste and adjust seasoning.
Serve hot, topped with fresh parsley.