Move the rack to the top position in your oven. Preheat the oven to BROIL. Line a baking sheet with tin foil. (note: do not use parchment paper -- if it gets too close to the broiler element, it will catch on fire -- ask me how I know that!!!)
Use a sharp knife to slice the grapefruit in half cross-wise. Use a small paring knife or bird's beak knife to loosen the grapefruit segments from the pith. Place the grapefruit on the prepared baking sheet.
In a small bowl, combine the sugar, cinnamon, cardamom and powdered vanilla (if using). Sprinkle one tablespoon of sugar mixture evenly over each grapefruit.
Transfer the grapefruit to the broiler and broil for 4-5 minutes or until the sugar is melted and slightly caramelized. Serve.
Note: you can also use a kitchen torch to achieve this, but you still want to heat the grapefruit for several minutes in a hot oven... this releases more juices and warms the fruit all the way through (if you just melt the sugar on top of the grapefruit the interior of the fruit would remain at room temperature.)