Peel 8 medium russet potatoes (4 pounds). Quarter lengthwise; cut crosswise 1/2 inch thick. In a 5-quart saucepan, combine potatoes and 1 head peeled garlic cloves (about 15); cover with water (about 8 cups) by 1 inch. Add 1 tablespoon coarse 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 11/2 cups milk to a boil; pour over potatoes. Add 1/2 cup (1 stick) butter, cut into small pieces, and 1 teaspoon salt. Mash until smooth and creamy.