Heat oven to 400°F. Cut top off garlic bulb; place bulb on piece of foil. Drizzle exposed top end of bulb with oil; sprinkle with 1/4 teaspoon each of the salt and the pepper. Wrap garlic in foil. Bake 50 to 55 minutes or until roasted. Unwrap and squeeze softened garlic into small bowl; mash with fork.
Meanwhile, in 2-quart saucepan, melt butter over medium heat, stirring frequently. Cook 2 to 5 minutes longer, stirring often, until butter stops foaming and browned bits form at bottom of pan. Remove from heat. Cool. Stir garlic into cooled butter.
In 3-quart saucepan, place potatoes and enough water to cover. Heat to boiling; reduce heat to medium. Cover loosely; boil gently 15 to 20 minutes or until potatoes break apart easily when pierced with fork. Drain well and return to saucepan.
Heat potatoes over low heat 1 minute to dry potatoes, shaking pan to keep potatoes from sticking and burning. Add browned butter; mash gently with potato masher. Remove from heat. Add milk and remaining 3/4 teaspoon salt and 1/2 teaspoon pepper. Mash until potatoes are light and fluffy. Sprinkle with cheese and chives.