Preheat the broiler.
Remove some of the grapefruit peel for a twist garnish, then cut the grapefruit in half. Place the grapefruit halves on a baking sheet flesh-side up and sprinkle the sugar evenly over the tops. Place under the broiler until the sugar is caramelized, about 6 minutes.
Meanwhile, fill a highball glass with ice and add the vodka. Remove the toasty grapefruit and squeeze the juice into the glass. Top with the ginger ale and garnish with the grapefruit twist.