Cut each grapefruit in half crosswise. Cut a thin slice off the bottom of each half, if necessary, so that it will stand upright.
Using a serrated grapefruit knife or a small sharp knife, loosen the grapefruit segments in each half by first carefully cutting between the fruit and the rind and then by cutting along either side of each segment.Place the halves upright on the broiling pan.
In a small bowl, stir together the brown sugar, cinnamon, and butter until well combined. Evenly sprinkle the sugar mixture over the grapefruit halves.
Place the broiling pan on the upper level.
Turn on Broil/Grill function. Cook for 7 minutes, or until the sugar is bubbly and caramelized.
Serve immediately garnished with a mint sprig if desired.