Peel the potatoes and cut them into evenly sized chunks; rinse briefly to remove excess starch.
Place potatoes in a large pot and cover with cold water by about an inch; stir in 1 teaspoon salt.
Bring to a boil, then reduce to a gentle simmer and cook until very tender, 15 to 20 minutes.
Warm the milk and butter together in a small saucepan or microwave until the butter melts; keep warm.
Drain the potatoes well, return them to the hot pot, and let steam off for 1 minute.
Mash the potatoes, slowly pouring in the warm milk-butter mixture until smooth and creamy.
Fold in the sour cream and garlic, then season with remaining salt and the pepper to taste.
Top with chives and serve hot.