In a medium saucepot, combine the potatoes, garlic and 1 tablespoon salt. Add cold water to cover by 2 inches. Bring to a boil and cook until the potatoes are easily pierced with a knife, 15 to 20 minutes.
Strain the potatoes and garlic and then rice them back into the pot. Add the milk, chicken stock, white pepper and 1 1/2 teaspoons salt. Place the pot over low heat and stir until the mixture comes together and is heated through. Remove from the heat and mix in the butter until melted in.
Serve immediately or wrap in foil and hold in a low oven.