With a sharp paring knife, slice off ends of grapefruits, oranges, or lemons. Following curve of fruit, cut away outermost peel, leaving most of the white pith on fruit. Slice peel lengthwise into 1/4-inch-wide strips.
In a medium pot of boiling water, cook peel until tender, about 10 minutes. With a slotted spoon, transfer peel to a wire rack set over a rimmed baking sheet; spread in a single layer to dry slightly, about 15 minutes.
In a medium saucepan, bring 1 cup sugar and 1 cup water to a boil over high, stirring to dissolve sugar. Add peel and boil until it turns translucent and syrup thickens, 8 to 10 minutes. With slotted spoon, transfer peel to wire rack, separating the pieces as needed.
Let peel dry 1 hour. Toss with 1/2 cup sugar to coat.