Wrap the garlic in foil and place in an oven at 375 for about 20-30 minutes until the head is soft when you squeeze it.
Meanwhile, peel and cut the potatoes and place in cold water. Bring the pot of potatoes up to a boil and cook until a piece of potato can be easily mashed with the back of a spoon. It will take about 15-25 minutes. Strain the potatoes, keeping at least 2 cups of the cooking liquid. To do this, I place my colander over a large pot or bowl in the sink and I am able to save most of the cooking liquid without burning myself.
Once the garlic is cooked through, place it in a cool spot until you can handle it (such as your freezer or in cold weather outside).
Return the potatoes to the pan. Start to mash them your favorite way. I typically use a potato masher, but occasionally I will grab a large wire whisk, potato ricer, food mill, or a pastry cutter. Keep the slightly smashed potatoes warm.
Once you can handle the garlic, peel each clove and place in a blender. Pour in about 1 cup of the cooking liquid and blend until smooth. Fold it into the potatoes and mash more, until it is your desired consistency. If you want them to be smoother, add more cooking liquid.
Fold in the olive oil, salt and pepper. Taste. Add more of each of those flavors as desired. Serve with a drizzle of olive oil across the top.
(If you love dairy, feel free to add a generous dollop of your favorite kind, such as creme fraiche, mascarpone, sour cream, greek yogurt or even heavy cream.)