Combine first 6 ingredients in a medium bowl, stirring well. Shape mixture into 4 (4-inch) patties.
Cut 4 (18- x 12-inch) pieces of heavy-duty aluminum foil; coat with cooking spray. Place a meat patty on one end of each piece of foil; place potato and onion evenly over patties. Top evenly with carrot.
Combine broth and remaining 7 ingredients, stirring well. Spoon broth mixture evenly over vegetables. For each packet, fold free end of foil over meat and vegetables; bring edges of foil together. Fold over to seal; pleat and crimp to make an airtight seal.
Place grill rack over medium coals (300° to 350°). Place packets on rack; grill 15 to 20 minutes or until packets are puffed. Remove packets from grill. Cut an opening in the top of each packet, and fold foil back. Remove patties and vegetables from foil, and transfer to serving plates. Top evenly with remaining juices.