Heat the Instant Pot using the sauté function. Add the olive oil, onion, carrot, and celery. Sauté, stirring occasionally, until the onions are just starting to soften, about 5 minutes.
Next add the garlic, broccoli, and chicken stock. Attach the lid and ensure the valve is in the sealing position. Pressure cook on high for 2 minutes.
Once the Instant Pot has finished cooking, release the pressure manually by switching the valve to the venting position.
In a small bowl, stir together the cheese, flour, and cornstarch.
Switch the Instant Pot back to the sauté function and add the cheese, a little at a time, stirring constantly.
Once all of the cheese has been incorporated, add the cream and cook the soup for 2-3 minutes, or until it has thickened slightly.
Enjoy immediately, topped with more cheddar cheese if desired.
Notes
Store any leftover soup in an airtight container in the fridge for up to three days.