Wash and peel potatoes, removing any eyes. Rinse and slice into quarters lengthwise. Place in an 8-quart stockpot. Add two inches of water and 1 tablespoon salt. Bring to a boil, reduce to a simmer, and cover until the potatoes are cooked through, 20-25 minutes.
Once the potatoes are cooked, remove them from the heat and drain. Reserve the potato water for another use. Pour the drained potatoes into a bowl and allow the steam to settle for 2 minutes. Using an electric hand mixer or mashing by hand, mash potatoes thoroughly. Add milk slowly and mix in, alternating with pieces of butter. Continue to mix until smooth.
Taste and adjust seasoning as needed, adding salt and pepper. Serve immediately as potatoes can become stiff the longer they sit.