Put the garlic cloves into a saucepan and cover with water. Bring to a boil, reduce the heat and simmer 30 minutes. Drain.
Cool slightly and press the garlic out of the skins into a small bowl.
Cut the potatoes into quarters and steam over boiling water 20 to 25 minutes, or until tender. Drain and put into a large bowl. With an electric mixer beat the hot potatoes until well mashed. Beat in the garlic, cream cheese, sour cream, milk, green chilies, salt and 2 tablespoons butter or margarine.
Beat until smooth and fluffy. Transfer to a greased 2-quart casserole and cool. Cover and refrigerate up to 24 hours ahead. Remove from refrigeration 1 hour before cooking.
Dot with 1 tablespoon butter and bake, covered, in a preheated 350 degree oven 30 minutes.
Uncover and continue baking 25 additional minutes.
Note: For those who like very spicy food, substitute a 4-ounce can of chopped jalapeno chilies for the chopped green chilies.