Combine all the ingredients up to the broccoli slaw in a medium bowl and stir with a whisk. Add the broccoli slaw and toss to combine. Refrigerate while you make the sliders.
For the salmon sliders:
Preheat a large skillet over medium heat. Preheat the oven to 180 degrees F and place a baking sheet on the center rack.
In a large bowl, combine all ingredients from the salmon through the walnuts Use a fork or your hands to thoroughly incorporate the ingredients. Gently shape into cakes that are about ½’’ thick and 3’’ in diameter.
Add oil (canola, olive, etc) to the preheated skillet to completely cover the bottom of the skillet. Use a spatula to transfer the cakes to the pan in batches. Cook the cakes for 3 minutes on each side. Transfer the cakes to the baking sheet in the oven to keep warm until you have cooked all of the cakes. Add olive oil to the pan as needed as you batch fry all of the cakes.
Serve the cakes on warm slider buns and top with broccoli slaw.