Place the salmon in a food processor and pulse it until it resembles a course ground meat, about 3 seconds. Transfer the salmon to a bowl and add the dijon mustard, lemon juice, chives, sea salt, black pepper, and cayenne. Gently combine. Divide the mixture into 4 to 6 equal parts, depending on how large you like your burgers, use your hands to form the patties.
On the stove top, preheat a 12-inch cast iron pan over medium-high heat. When the pan has warmed, add the oil. Place the patties inside of the pan and cook until each side is golden brown and cooked through, about 3 to 4 minutes.
To assemble the slaw, place the cabbage and broccoli slaw in a large bowl and set aside. In a wide mouth mason jar combine the avocado, water, lemon juice, apple cider vinegar, chives, salt, garlic powder, and chopped onion. Use an immersion blender to puree until smooth. Pour the dressing over the slaw mixture and toss to coat. Serve the salmon burgers over the broccoli slaw.