Grease a 3-quart ovenproof dish with 1 Tbsp. butter. In a large pot, cover potatoes and garlic with cold water and add 2 tsp. salt. Bring to boil and cook over medium heat until tender, about 30 minutes. Drain and return potatoes and garlic to pot.
While potatoes are cooking, bring cream, grated Parmesan and 2 Tbsp. butter to simmer in a medium saucepan, stirring until Parmesan melts. Remove mixture from heat and set aside. Preheat oven to 350°F.
Mash potatoes and garlic with cream cheese until smooth. Add cream mixture to potato mixture and stir well to combine. Stir in chives, season with salt and pepper and spoon potato mixture into prepared baking dish.
Dot potatoes with remaining 1 Tbsp. butter and bake until potatoes are heated through and golden brown on top, about 45 minutes. Serve immediately.