Put the potatoes in a medium saucepan and pour in enough cold water to cover them by a couple of inches. Toss in a handful of salt. Bring the water to a boil and cook until the potatoes are tender when poked with a knife, about 25 minutes.
Drain the potatoes and return to the pan. Add the cream and butter and let the whole pot sit over very low heat until warmed through.
Add chives and basil to the pot with the potatoes and mash the potatoes coarsely. Season with salt and pepper.