Peel potatoes and quarter lengthwise; cut crosswise 1/2 inch thick. In a 5-quart saucepan, combine potatoes and garlic cloves; cover with water (about 8 cups) by 1 inch. Add 1 tablespoon salt.
Bring to a boil; reduce heat, and simmer until potatoes are easily pierced with the tip of a paring knife, 25 to 30 minutes.
Drain; return garlic and potatoes to pan. Stir over medium-high heat until dry, 1 to 2 minutes. Remove from heat.
In a small saucepan, bring milk to a boil; pour over potatoes. Add butter and 1 teaspoon of salt. Mash until smooth and creamy.