In small saucepan set over medium-high heat, combine blueberries, onion, sugar, apple cider vinegar, and allspice; bring to a boil. Reduce heat to medium; cook, stirring often, for 8 to 10 minutes or until thickened to syrupy consistency. Let cool completely.

Grill patties according to package directions. Serve in buns topped with Blueberry Ketchup, Brie, arugula, red onion, and radishes.