1. Make burgers: In a large bowl, combine beef, parsley, shallot, salt, garlic powder, Worcestershire sauce and cayenne. Using your fingers, mix gently but thoroughly. Divide meat mixture into 16 disks. Portion cheese into 8 small disks and place in the center of 8 hamburger disks. Top with remaining hamburger disks, pressing to seal.
2. Make sauce: In a bowl, combine ketchup, dressing, pickle and hot sauce. Cover and chill until ready to serve.
3. Preheat grill to medium. Grill hamburgers for about 7 minutes (for medium-rare), turning once. Remove from heat and let rest for 2 minutes. Grill buns, cut sides down, for 30 seconds.
4. Serve burgers on buns with sauce, lettuce, tomato and onion.