Place potatoes and garlic in a large pot and cover with cold water by 1 inch. Add 3 teaspoons salt. Bring to a boil over medium-high heat, then reduce to a simmer and cook until very tender, 15–20 minutes.
Drain well and return potatoes and garlic to the hot pot over low heat for 1–2 minutes to evaporate excess moisture.
Mash potatoes and garlic with a masher or ricer until smooth.
Stir in butter and remaining 1 teaspoon salt until butter melts.
Gradually mix in warm milk until creamy, adding more if a looser texture is desired.
Transfer to a serving bowl, sprinkle with chives, and serve hot.
