Quarter grapefruit and remove rinds; use interiors for another purpose. Slice each rind lengthwise into strips, approximately 1/4 inch at the widest point.
Cover rind with 2 inches of water in a heavy saucepan. Bring to a boil; boil for 3 minutes. Drain. Repeat 3 more times with fresh water. Drain.
Place boiled grapefruit rind, 1 3/4 cups sugar, and 1 cup of fresh water into the saucepan. Let simmer slowly, increasing heat as needed, until water is absorbed or evaporated, about 1 hour.
Place remaining 1 cup sugar in a large bowl and toss peels in it. Cool and allow to dry on wax paper or a wire rack. Dust with more sugar as preferred.
Cook's Note:
You can use white or pink grapefruit. I have had the best batches from grapefruit that has thinner, rather than thicker, rinds. The thicker rinds tend to stay very moist.