Set instant pot to sauté.
Add olive oil to instant pot and heat it up.
Stir in smashed garlic cloves; mix and stir until garlic is golden brown on all sides, about 1 minute.
Stir in chicken broth and cook for 1 minute.
Turn off the "sauté" mode and place steamer basket inside your Instant Pot.
Transfer prepared cauliflower to the basket inside the Instant Pot.
Close the lid and set the valve to sealing.
Set on manual setting and cook on high pressure for 3 minutes.
Use the quick release function to release the pressure. Open up the lid half way and let stand 3 minutes.
Drain out all of the liquid and transfer the cauliflower and garlic to a food processor or blender. You can also put it in a large bowl and use a potato masher.
Add butter, sour cream, salt, and pepper to the blender; process until blended and creamy. I recommend using the pulse function because you have more control over how creamy or chunky you want your mashed cauliflower.
Transfer the cauliflower mixture to a mixing bowl or serving dish.
Stir in parmesan cheese and chives. Taste for seasonings and adjust accordingly.
Garnish with fresh chives and serve.