Set oven to BROIL. Cut the grapefruit in half or in thick slices.
Stir together the sugar and crystallized ginger. If you prefer, the sugar and crystallized ginger can be ground in a coffee mill/spice grinder.
Spoon the sugar mixture onto the grapefruit slices. Add a few drops of vanilla extract to each slice. Or, if using vanilla paste, spread a little bit on each grapefruit slice first then add the sugar mixture.
BROIL the grapefruit for about 3-5 minutes until the sugar starts to bubble. Watch carefully to avoid burning!