Cut grapefruits horizontally in half. Using grapefruit knife or paring knife, cut all around grapefruit halves and between membranes to release segments. Place segments in bowl, discarding seeds. Cut segments in bowl, discarding seeds. Cut all membranes from 6 grapefruit halves; discard remaining grapefuit halves.
Place large scoop of ice cream in each reserved grapefruit half. Cover and place in freezer until ready to use. Add sugar and ginger to grapefruit in bowl and toss gently. Cover and refrigerate at least 2 hours or overhight.
Spoon some grapefruit mixture over ice cream in each grapefruit basket. Garnish with mint. Serve, passing remaining grapefruit mixture separately.
SOURCE: BON APPETIT, April '93