Peel the potatoes and cut into uniform 1/2-inch pieces. Place into a 4-quart saucepan and cover with cold water by at least 1 inch. Cover, set over high heat, and bring to a boil. Once boiling, remove the lid, decrease the heat to maintain a simmer, and cook until the potatoes can easily be crushed with a pair of tongs, 15 to 20 minutes. Drain in a colander.