Peel potatoes and cut into even chunks for quick, even cooking.
Place potatoes in a pot and cover with cold water by 1 inch. Stir in 1 tsp salt.
Bring to a boil, then simmer until very tender when pierced, 15–18 minutes.
Warm milk, butter, and garlic in a small saucepan over low heat until steaming.
Drain potatoes well, return to the pot, and let steam off for 2–3 minutes.
Mash potatoes, then slowly pour in about half the warm milk-butter mixture.
Fold in sour cream. Add more warm milk to reach a smooth, creamy texture.
Season with remaining 1/2 tsp salt and the pepper. Sprinkle with chives and serve hot.