Prick each sweet potato several times with a fork. Place on a rimmed baking sheet, preferably lined with parchment or aluminum foil, and bake until tender, about 1 ¼ to ½ hours.
Meanwhile, prepare the garlic for roasting. Cut the top from the head of garlic with a sharp knife, exposing the very tops of the cloves. Place the garlic head on a square of aluminum foil large enough to encase the garlic. Drizzle 1 tablespoon of the olive oil over the exposed top of the cloves. Sprinkle the top with salt. Wrap tightly in foil, and after the sweet potatoes have been in the oven for 30 minutes place the foil-wrapped garlic on the baking sheet with the squash. Continue baking the potatoes and the garlic for about 45 minutes until the garlic and the potatoes are very soft. Let the garlic cool in the foil, and let the potatoes cool until you can handle them.
When the vegetables are cool enough to handle, unwrap and squeeze out the roasted garlic from the papery wrapper, pressing up from the bottom to pop it out. Peel the sweet potatoes (you should be able to peel the skin off with your fingers, or use a peeler if you feel like you are losing too much of the insides).
Press the garlic and the potatoes together through a food mill or a ricer into a large pot over medium heat. If you don't have either, you can place them in a large pot and use a potato masher. Add the remaining olive oil, butter, milk, salt, and pepper and stir to thoroughly combine. Heat, stirring, frequently until hot throughout.