Preheat the over to 500, rub the garlic with oilive oil, wrap in foil and bake for 45 minutes. Remove and let cool. When cool enough to hanle, squeeze the soft roasted garlic and place in a bowl.
In a large saucepan, cover the chopped potatoes with cold water. Bring to a boil. Reduce heat and cook until the potatoes are tender, about 15-20 minutes. Drain well.
Return thepotatoes to the saucepan. Add the cream and butter and with a hand mixer, blend until smooth. Do not over-whip the potatoes, just till smooth.
Add the roasted garlic and the chopped basil. Season with salt and pepper.