Place the potatoes in a large pot, cover with cold water by 1 inch and add the tablespoon salt. Bring to a boil, then simmer for 15 to 20 minutes until a knife slips easily through the largest pieces.
Warm the milk and butter in a small saucepan over low heat until the butter melts; keep below a boil.
Drain the potatoes thoroughly and return to the warm pot over low heat for 1 minute, shaking gently to dry their surfaces.
Mash by hand, then fold in the warm milk mixture a little at a time until the potatoes are fluffy and spoonable.
Fold in the remaining salt and white pepper. Transfer to a warm serving bowl and serve while hot.