Place potatoes and 1 tablespoon of the salt in a large saucepan; cover potatoes with cold water, about 6 cups. Bring to a boil over high, and reduce heat to medium. Partially cover pan, and simmer until potatoes are just tender enough to pierce with a fork, about 20 minutes. Drain well, and return to warm pan. Let stand 5 minutes.
Mash potatoes with a handheld potato masher or a large fork. Stir in warm milk, butter, and mustard. Stir in pepper and remaining 2 1/2 teaspoons salt. Serve immediately.