Skin and cube up your salmon. Then run a chopping knife through the cubed salmon until the bits are small but not to a puree. The texture should resemble that of ground beef.
Combine the chopped salmon and salmon burger seasonings in a medium mixing bowl. Place in the fridge while you prepare the aioli.
To make the aioli, put all of the aioli ingredients into a pint mason jar, and blend with an immersion blender. If you don't have an immersion blender, you can blend everything except the oil with your food processor, and then drizzle the oil in slowly while it blends. Set the aioli aside in the fridge while you cook the salmon burgers.
Heat a skillet with your friendly cooking fat of choice over medium-high heat while you form your salmon burgers.
Divide the salmon mixture into the sized burgers you want, and form burger patties with your hands. This takes just a little bit of time, but it is worth working the patties gently so they come together and aren't too overworked.
Dust the salmon burgers on both sides in a small bowl of potato starch. Place the potato starch dusted salmon burgers into the hot oil, and cook over medium to medium-high heat for 5 minutes. Flip the burgers and cook another 3-5 minutes, until both sides are golden brown, crispy on the outside, and cooked on the inside. If you make smaller salmon burgers your cook time will be shorter - this cook time was for 1 pound of salmon formed into 4 burgers.