Mix the burgers. Combine the ground chicken, onion, mayo, dijon, Worcestershire, liquid smoke, garlic powder, and salt and pepper together in a mixing bowl. Mix gently by hand until just combined and all the ingredients are evenly mixed.
Shape the patties. Divide the mixture into 4 and shape into patties with a depression in the middle. Place the shaped burgers on a plate or small baking sheet lined with parchment paper. Transfer the burgers to the freezer for 15-20 minutes, until firmed up.
Cook the burgers. Heat a grill pan or cast iron skillet over medium heat. Let the pan preheat for about 5 minutes. Add a bit of neutral oil. Once the oil is hot, cook the burgers for about 5 minutes per side, until browned. Add the cheese after flipping the burgers so that it has time to melt. Use a meat thermometer to ensure the burgers are cooked to 165 F.
Grill the onions. Remove the burgers from the skillet or grill pan and use the same pan to cook the onions for 4-5 minutes per side, until soft and browned. Season the onions with salt and pepper.
Build the burgers. Toast the buns and top with the juicy chicken burgers and grilled onions and any other desired toppings.