Preheat oven to 400 degrees.
Arrange garlic in 1 layer on a double thickness of foil and wrap tightly.
Roast the garlic and potatoes in middle of the oven
The garlic will take 45 minutes and the potatoes will take 1 hour.
Unwrap the garlic and cool sightly. Peel the cloves, mash with a fork, and set aside.
Combine The milk and butter in a large bowl. Scoop the potatoes out from the skin into a bowl and mash using a potato masher. Save the skins and Julienne them.
Sprinkle the skins with olive oil, place back in 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 mashed potatoes with the crisp potato skins.