Place the potatoes in a large saucepan, add enough cold water to cover the potatoes and cover the pot. Heat on high, bring the water to a boil. Reduce heat to medium and simmer until potatoes can be easily pierced with a knife, about 20 minutes. While the potatoes are cooking, combine the cream, butter and basil in a small saucepan and heat over medium heat until the butter is melted and the cream is hot.
Drain the potatoes and allow them to sit in the colander for a couple of minutes. Place the potatoes in a mixing bowl and mash. Stir in the cream mixture by thirds. Season with salt and pepper to taste.