Place potatoes in a large Dutch oven; cover with cold water by 1 inch. Place pan over medium-high. Bring to a simmer; cook potatoes 17 minutes or until completely tender. Drain well. Return potatoes to pan; place over medium-low. Cook 5 minutes or until all the liquid has evaporated, stirring occasionally (do not brown). Place potatoes in a food mill or large colander with medium-small (1/8-inch) holes.
Combine milk and butter in pan over medium-low; cook until butter melts, stirring occasionally. Set mill or colander over pan; crank mill, or use the back of a ladle or large spoon to press cooked potato through colander into milk mixture. Add salt and pepper to milled potato in pan; stir well to combine.