To make the slaw, in a medium bowl, add the kimchi, cabbage, kimchi juice, and a pinch of salt and toss to combine.
To make the sauce, in a small bowl, add the remaining scallions, yogurt, sesame, kimchi juice, gochujang (if using), and salt and stir to combine.
To make the patties, in a large bowl, add the chicken, scallions, soy, gochujang, sugar, sesame oil, garlic, and ginger. Use your hands to mix until thoroughly combined.
Form the mixture into 4 large patties (or do smaller ones). In a large skillet over medium heat, warm 1 tablespoon olive oil. Once the oil is hot and shimmering, place the patties in the skillet and cook for about 3-5 minutes per side or until cooked through and charred or browned on each side. Adjust the heat if it’s burning too quickly.
For a burger: mash avocado onto the bottom bun. Top with the slaw, then the patty, then the sauce.
For a bowl: serve the patty over warm rice and top with the slaw, avocado, and a squeeze of lime. Sprinkle chopped cilantro or scallions on top, if you have any.