Preheat grill to 350° to 400° (medium-high) heat. Combine first 5 ingredients gently. Stir olives into meat mixture. Shape mixture into 6 (5-inch) patties.
Grill, covered with grill lid, 6 to 7 minutes on each side or until a meat thermometer inserted into thickest portion registers 170°. Pulse pickled vegetables and Italian dressing in a food processor until coarsely chopped. Serve burgers on Homemade Hamburger Buns. Top each burger with vegetable mixture and salami, ham, and provolone cheese slices.
Note: We tested with Mezzetta Italian Mix Giardiniera pickled vegetables.