Place potatoes in a colander and rinse under cold water until the water runs clear. Transfer potatoes to a large pot and fill with enough cold water that potatoes are covered by 2 inches; add 1 teaspoon salt. Bring to a boil, then lower heat to medium and cook until fork-tender, about 20 minutes.

Drain potatoes in a colander and transfer to a large bowl or the bowl of a stand mixer. Add remaining ½ teaspoon salt, garlic, 6 tablespoons butter, cream cheese, sour cream, and ½ cup milk. Using an electric hand mixer, or in a stand mixer fitted with a paddle attachment, blend on medium speed. Pour in remaining ½ cup milk and mix on high speed to whip potatoes until fluffy.