In a small saucepan over medium heat, bring sugar and 2/3 cup water to a boil. Continue boiling until syrup reaches 238F on a candy thermometer (soft-ball stage).
Meanwhile, place egg whites in the bowl of a standing mixer fitted with the whisk attachment, and beat on low speed until foamy. Add cream of tartar, and beat on medium-high speed until stiff but not dry; do not overbeat.
With mixer running, add syrup to whites in a thin stream, beating on high speed until no longer steaming, about 3 minutes. Add butter bit by bit, beating until spreadable, 3 to 5 minutes; beat in vanilla and brandy. If icing curdles, keep beating until smooth.