POUR boiling water over figs in bowl; cool to room temperature. Pour figs and water into food processor container. Add barbecue sauce; process until smooth.
FOR each serving: Grill 1 turkey patty until done (165ºF). Place on bottom half of bun; top with 2 Tbsp. fig sauce, 1/4 cup arugula, 3 tomato slices, 4 avocado slices and 1 Tbsp. cheese. Cover with top of bun.