Heat the Instant Pot using the Saute-Normal function. Add the olive oil and unsalted butter.
Pat the chicken thighs dry with a paper towel and season them lightly with salt and pepper.
When the butter has melted, add the chicken thighs skin side down and cook for 2 to 3 minutes, or until the chicken has started to turn golden brown.
Flip the chicken thighs and cook for an additional 2 minutes.
Turn the Instant Pot off. Add the trivet to the bottom and place the chicken thighs, skin side up, on the trivet. Try not to overlap them too much.
Pour in the water or chicken stock. Set the Instant Pot to the Manual Pressure Cook-Normal-High Pressure for 10 minutes. Make sure the pressure valve is in the “sealing” position.
The Instant Pot will take a few minutes to come to pressure and will then begin counting down from 10.
When the Instant Pot has finished cooking, manually release the pressure by switching the valve to the “venting” position. Be careful–the vent will steam and may splatter.
Remove the chicken thighs and set them aside. Remove the trivet and discard the water/stock.
Heat the Instant Pot using the Saute-Normal function. Add the unsalted butter, olive oil, garlic cloves, and red pepper flakes, if using.
When the butter has melted and the garlic has started to turn golden, add the parmesan and fresh chopped parsley and stir to combine.
Return the chicken thighs to the Instant Pot and toss to combine–make sure the chicken thighs are coated on all sides with the garlic parmesan sauce.
Serve immediately.