Preheat oven to 350 degrees F. Place garlic head in a 6 oz custard cup or small baking dish and drizzle with oil. Bake, uncovered, until garlic is soft and fragrant, about 40 minutes.
Meanwhile, place the diced potatoes into a large saucepan. Add cold water to the pan until the potatoes are covered by at least an inch of water. Add some salt to the water. Bring the water to a boil over high heat. Reduce the heat to low, cover and simmer for 15 to 20 minutes, or until potatoes are fork tender. Drain potatoes.
Add Greek yogurt, cream cheese, butter, salt and pepper to potatoes. Squeeze roasted garlic from cloves into potato mixture.
Mash potatoes using a potato masher until smooth and creamy, and thoroughly combined. You can also whip the potatoes briefly with a hand beater for a creamier consistency. Garnish with a sprinkle of parsley.
Taste and adjust flavors accordingly, adding more Greek yogurt or a bit of milk if you want the potatoes creamier, additional butter if you like them more buttery, or more salt, pepper or parsley to incorporate additional flavor.