Preheat the oven's broiler and set the oven rack about 6 inches from the heat source.
Combine the white bread, garlic, and boiling water in a mixing bowl; mash with a fork to combine. Add the turkey, red onion, cranberries, Brie, rosemary, ketchup, salt, and pepper; mix thoroughly with your hands. Shape the mixture into 6 patties.
Cook under the preheated broiler until no longer pink in the center and the juices run clear, about 6 minutes per side. An instant-read thermometer inserted into the center should read at least 165 degrees F (74 degrees C).