Preheat the oven to 400°. Rub the garlic head with the olive oil.
Wrap in foil and bake for 45 minutes. Remove and let cool.
When cool enough to touch, squeeze out the garlic into a small bowl
and set aside. The garlic should be the consistency of thick
toothpaste.
In a large saucepan, cover the chopped potatoes with cold
water and bring to a boil. Reduce heat to medium and cook until
potatoes are very tender when stabbed with a fork, about 15 minutes.
Drain well. Return to the saucepan and add the cream and butter.
With a hand mixer, blend until just smooth (do not over-whip).
Add the reserved garlic and the chopped basil.
Garnish each serving with small whole basil leaves.
Season generously with salt and pepper and serve immediately.