Peel and cut the potatoes into equal sized chunks. Rinse with cold water and drop into the boiling water.
While the potatoes are boiling, combine the butter and milk or heavy cream in a small saucepan and warm just until the butter melts.
Cook until the potatoes are cooked through – a paring knife easily pierces all the way through the chunk. Strain the potatoes and rinse briefly with water. Strain again.
Transfer the potatoes to a food mill or ricer and press the potatoes through into a bowl. Add the warm butter and milk or cream and stir into the potatoes. Season well with salt and freshly ground pepper and keep warm until serving.