Preparation

1. In a large pot, bring a gallon of water and 2 tablespoons salt to a boil over high heat. Peel and quarter potatoes and keep in cold water until ready to cook. (This can be done up to 4 hours in advance.) Add potatoes to boiling water and boil about 15 to 20 minutes, until soft; a knife should go in with almost no resistance. (It is better to overcook than to undercook.)

2. In a saucepan or a microwave oven, heat butter and milk together until butter melts and mixture steams. Drain potatoes well and return to pot. Shake them around in the hot pan or over very low heat for a minute (you want dry potatoes). Using an extruding masher or a ricer, mash hot potatoes until smooth, about 2 minutes. Lightly mix in about half of hot butter mixture, just until blended. Taste for salt and add more butter mixture until seasoned to your liking.

3. Stop here for fluffy potatoes. For creamy potatoes, keep stirring potato mixture, using a sturdy spoon to press it against sides and bottom of pot. Mix until dense and thick. For whipped potatoes, use a stand mixer to mash hot potatoes just until smooth, about 30 seconds. Add all the butter mixture and salt to taste, pulsing machine in short bursts at medium speed. When light and creamy, stop mixing immediately. (Potatoes can quickly become sticky.)

4. To keep hot until ready to serve, transfer to serving bowl, dot top with butter, cover tightly and keep in a warm place, like the back of the stove. Potatoes will stay hot for at least 30 minutes. To keep longer, place covered bowl in a pan holding about an inch of gently simmering water. Before serving, mix well.