The bowls can be prepared one to two days in advance; the syrup produced during preparation can be used to sweeten drinks or be reduced and used as a glaze.
Cut off the tops of the grapefruits a third of the way down from the stem end. Place trimmed bottoms in an 8-quart stockpot; cover with 3 quarts water. Cover surface of water directly with a piece of parchment paper cut to the same size as the diameter of the stockpot. Bring to a boil; reduce heat, and simmer, uncovered, for 2 hours.
Remove grapefruits; place upside down on a wire rack to drain. Reserve parchment round. When cool enough to handle, scoop out flesh with a spoon (do not puncture grapefruit skin). Discard flesh.
Combine sugar, corn syrup, and 3 3/4 cups water in the stockpot; bring to a boil over medium-high heat, using a wet pastry brush to incorporate sugar crystals that form on the side of pot. Clip a candy thermometer to pot; cook until syrup reaches thread stage (230 degrees). Add grapefruit bowls; reduce heat. Cover with reserved parchment round, and simmer for at least 1 hour, occasionally turning gently. Grapefruits should be unevenly translucent. Turn off heat; let cool in syrup until completely translucent, about 2 hours. Using a whisk small enough to fit in the bowls, gently lift grapefruits from syrup. Place upside down on a rack over a baking sheet. Let dry overnight. Store in an airtight container lined with parchment.