Line a baking sheet with parchment paper, set aside.
Mash the chickpeas in a large bowl until there are no whole chickpeas left. Using your hands, mix in the turkey, bread crumbs, egg, mustard, Worcestershire sauce, garlic, 1 tablespoon olive oil, 2 teaspoons salt, 1 teaspoon black pepper. Form four to size 1-inch thick patties (about 1/2 cup each) and place on the lined baking sheet.
Heat the remaining 2 tablespoon olive oil in a large nonstick skillet over medium heat. Add the patties and cook until golden brown and opaque throughout, 3 to 4 minutes per side. Top each patty with a slice of cheese, cover and cook until the cheese has melted, about 1 minute. (You can also do this step in batches.)
Serve the burgers on toasted buns with mayonnaise, mustard, lettuce and tomato slices.