Combine the chicken, panko, mayonnaise, egg, dill, mustard, lemon zest and 1/2 teaspoon each salt and pepper in a bowl. Gently form into eight 3/4-inch-thick patties, then freeze until firm, about 10 minutes.
Sprinkle some panko on a plate. Coat the patties on both sides in the panko, pressing gently to adhere.
Heat the butter and olive oil in a large skillet over medium-high heat. Add the patties and cook until golden, 3 to 4 minutes per side. Transfer to paper towels to drain and season with salt. Serve with lemon wedges.