Preheat the oven to 400°. Cut the top of the head of the garlic off to expose the cloves (about ½ inch). Drizzle lightly with olive oil.
Wrap the head of garlic in foil. Roast for 30 minutes.
Remove the foil from the garlic.
Roast for another 15 minutes unwrapped. Set aside and let the garlic cool.
While the garlic is roasting unwrapped, you will cook the potatoes. Place the potatoes and the chicken broth in the Instant Pot. Season the liquid with a pinch of salt. Place the lid on the pot and turn the valve to “sealing”. Select the pressure cook or manual setting, high pressure, and set the timer for 10 minutes. The Instant Pot will begin coming to pressure and show the timer once it reaches the correct pressure.
After the garlic finishes roasting, let it cool. Once you can handle the garlic, squeeze each clove out of the head into a bowl. Mash them with a fork. Set aside.
After 9 minutes, switch the valve to “venting”. The pot will release steam and the lid will unlock. Remove the lid and set the pot to the “keep warm” setting. Drain the excess liquid from the potatoes and place back in the pot.
Add the butter, half and half, sour cream, cheddar cheese, salt, and pepper.
Mash until smooth using a rice or potato masher.