Slice off top of garlic head, barely cutting of the top of each clove.
Take a piece of aluminum foil and scrunch it into a snake. Wrap this around the side of the garlic head.
Brush the top of the garlic head with the oil, roast in oven until top of cloves are golden brown and the cloves look to have separated from the side walls of the head, about 1 hour.
Meanwhile, wash and Peel the potatoes. Split in half, then cut half into four similarly sized pieces.
Place potatoes in a large, deep pot. Add enough water to come one inch over the potatoes. Cover, and bring to a boil over high heat. Keep and eye on the pot, so as to prevent boil-overs.
Boil until a paring knife can easily stab through a potato piece. When appropriate doneness is reached, drain and pour into the workbowl of a stand mixer (or keep in the pot and use a hand mixer.)
Whip the potatoes alone on high speed until thy are all broken down. Add the butter, continue to whip for 1-2 more minutes. It is important that the butter be added first - this will help to keep the starches in the potato from becoming gummy or gluey.
Slowly add the Buttermilk while the mixer is going. Slowly add the half-and-half, stopping periodically to see if he potatoes actually need the extra moisture. They may need more or less than perscribed, it is really a matter of personal preference.
Squeeze the roasted garlic cloves into the mashed potatoes, add the salt and pepper to taste. Mix thoroughly.