Prepare the cheese, onion, and parsley. Prepare the following, transferring to a large bowl: Grate ½ ounce Parmesan cheese on the small holes of a box grater until you have lightly packed ¼ cup. Grate ¼ medium red onion on the large holes of a box grater until you have 2 tablespoons. Finely chop ¼ cup fresh parsley leaves.
Mix the panade. Add ¾ cup bread crumbs, ¼ cup mayonnaise, 2 tablespoons Dijon mustard, ½ teaspoon garlic powder, and ¼ teaspoon black pepper, then mix with a silicone spatula until combined.
Mix in the chicken by hand. Add 1 pound ground chicken and use your fingertips to gently combine. Do not overmix.
Form into patties. Divide the mixture into 4 (6-ounce) portions. Form each into a patty that’s about ¾-inch thick and 4-inches wide. Place on a plate or baking sheet.
Chill the patties. Cover the patties with plastic wrap and refrigerate for at least 1 hour and up to 1 day.
Season the patties. Season the top of the patties with ¼ teaspoon of the kosher salt.
Cook the chicken burger patties. Heat 1 tablespoon vegetable oil in a large cast iron skillet or nonstick pan over medium heat until shimmering. Add the burgers salt side down (cook in 2 batches if needed so as not to crowd the pan). Season with the remaining ¼ teaspoon kosher salt and cook undisturbed until a golden-brown crust forms on the bottom, about 6 minutes.
Flip the burgers. Flip the burgers with a thin, flat spatula.
Top with cheese and finish cooking. Top each burger with 1 slice of cheese, if desired. Cook until the burgers are cooked through and register an internal temperature of 160°F, 5 to 6 minutes more.
Assemble the burgers. Assemble the burgers on hamburger buns with desired toppings such as lettuce leaves, sliced tomato, mashed or sliced avocado, and thinly sliced red onion.
