Cover potatoes with cold salted water in a large pot.
Bring to a boil, then simmer until easily pierced, about 12–15 minutes.
Warm milk and melt butter together on the stovetop or in the microwave.
Drain potatoes well and return to the hot pot to steam off moisture for 1 minute.
Mash potatoes to your preferred texture, then fold in pumpkin puree.
Stir in warm milk-butter mixture, garlic, salt, pepper, and nutmeg until smooth and fluffy.
Taste and adjust seasoning. Blend in sour cream if using.
Top with chives and serve hot.