Chop the salmon roughly into approximately 1/2 inch cubes.
Mix chopped salmon in a medium sized bowl with lemon zest (1 teaspoon), parsley (2 tablespoons), red onion (1/4 cup), mayonnaise (2 tablespoons), kosher salt, and pepper. Add 1/4 cup panko bread crumbs and if the mixture seems too wet, add more until you reach the desired consistency.
Form the mixture into four equal sized patties.
Heat the olive oil (2 tablespoons) in a heavy skillet (such as cast iron) to medium high heat. Sear the patties on one side for approximately 4 minutes. Flip and cook for another 4 minutes, or until salmon is cooked through.
Meanwhile, mix the ingredients for the lemon caper aioli in a small bowl.
Serve the patties on toasted burger buns topped with aioli and arugula.
For a lower-carb version, omit the bun and serve on lettuce wraps or on top of a bed of greens drizzled with the sauce.
When I buy salmon at the fish counter, I ask them to take the skin off for me. They do a much better job than I could, and the service is free! You may even be able to ask them to chop it up for you- I've never tried but I sure as heck will next time.
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