Heat the broiler for 10 minutes with the rack in the second-to-highest position.

Use a sharp paring knife to cut the fruit segments away from the membrane on both halves of the grapefruit. (This will make the fruit easier to eat, and let the agave infiltrate the fruit.) Place the grapefruit halves cut side up on a baking sheet. (If the grapefruit is sitting wobbly or crooked, slice a bit of the peel off from the base to steady it. Be careful not to cut past the pith into the fruit.) Divide the agave nectar and sugar between the grapefruit halves.

Toss the jalapeño with 1 tsp canola oil and a pinch of salt and add to baking sheet with the grapefruit. Broil 10 minutes, or until the grapefruit is bubbly and juicy, and jalapeño is charred in places.

Sprinkle the grapefruit with bit of chili powder and salt, and top with the jalapeño, cilantro, and mint.