Preheat oven to 400 degrees F.
Arrange garlic in 1 layer on a double thickness of foil and wrap tightly.
Roast the garlic and potatoes in middle of oven--the garlic will take 45 minutes and the potatoes will take 1 hour.
Unwrap garlic and cool slightly. Peel the cloves, mash with a fork, and set aside. (The garlic may be roasted and stored in the refrigerator, up to a week ahead.)
Combine the milk and butter in a large bowl. Scoop the flesh from the potatoes into the bowl and smash using a potato masher. Reserve the skins and julienne them.
Drizzle the skins with the olive oil, transfer to the oven, and bake until crisp, about 12 minutes.
Using a rubber spatula, mix the potato mixture and garlic together until creamy. Fold in the basil and season with salt and pepper. Garnish the smashed potatoes with the crisp potato skins.
Recipe adapted from Gourmet Magazine