Cover potatoes with cold water in a large pot. Stir in 1 tsp of the salt.
Bring to a boil, then simmer until the potatoes are very tender, 15–18 minutes.
Meanwhile, gently warm milk, butter, and garlic in a small saucepan until butter melts. Do not boil.
Drain potatoes well and return to the hot pot. Let steam off moisture for 1 minute.
Mash potatoes to your preferred smoothness using a masher or ricer.
Slowly pour in the warm garlic-butter milk, mashing and stirring until creamy.
Fold in Parmesan and sour cream. Season with remaining salt and the pepper.
Adjust consistency with a splash more warm milk if needed. Top with chives and serve hot.