Add half of the salmon, ¼ cup of mayo and 3 tablespoons of Dijon mustard to a medium sized food processor. Blend until it becomes a paste, about 1 minute.
Chop the remaining salmon into chunks. To the mixture add the rest of the salmon, cayenne, garlic powder, black pepper, lemon zest, red onion, dill, salt and breadcrumbs. Pulse until the chunks break down to smaller pieces and the mixture comes together, about 30 seconds.
Using a ½ cup measure, scoop the mixture and form into patties. Place on a baking sheet lined with parchment or wax paper. When all six are formed, put the burgers in the fridge to chill and make the mayo!
In a medium sized bowl add all of the ingredients for the Lemon Dill Mayo. Stir by hand until all combined. Add salt and pepper to taste. Put away in the fridge until you're ready to serve!
In a large saute pan add 2 tablespoons of olive oil and turn to medium heat. Add 2-3 salmon burgers (whatever you can fit without them touching) and cook for 4 minutes. Flip the burgers after that time and cook for an additional 3 minutes.
If you're eating these right away, I like to toast my buns while I'm cooking the burgers. Assemble with your toppings and the mayo and enjoy!