Preheat oven to 350 degrees F. Prepare two heads of garlic for roasting: Leaving garlic head intact, cut tip off of garlic cloves, exposing the flesh of each clove. Repeat with the second head of garlic. Place the heads root-side down on a sheet of aluminum foil. Drizzle oil over the exposed flesh. Wrap up the heads into a bundle and bake until fragrant and the garlic is tender, about 45 minutes. Open packet to vent and set aside to cool.
When the garlic is cool, squeeze the garlic out of the skins into a bowl and mash with a fork into a smooth paste. Mash in butter, pepper and the remaining ½ teaspoon salt. Stir in yogurt.
Meanwhile, peel the remaining 2 cloves garlic. Cover potatoes and the two cloves garlic generously with cold water in a large saucepan. Place over high heat and bring to a boil. Reduce heat to maintain a gentle simmer and cook until the potatoes are tender when pierced with a fork, 15 to 18 minutes. Drain and return to the pot. Mash potatoes with a potato masher. Add the yogurt mixture and mash until smooth. Transfer to a serving dish and garnish with parsley.
