Add all burger ingredients to a large bowl. Mix well to incorporate into mixture. I use my hands.
Heat oil in a large non-stick skillet over medium heat on the stove. Form patties with salmon mixture and place onto the skillet. Let patties cook until bottoms are slightly browned and then carefully flip to cook the other side until cooked through, about 5 minutes per side.
Meanwhile, in a small bowl, prepare sauce. Mix together greek yogurt, lemon juice, and dill. Set aside.
Thinly slice red onion and cut buns in half and toast them if you’d like.
Once salmon patties are cooked, assemble burgers: Place a small handful of arugula, a few slices of onion, and a sprinkle of feta on the bottom bun. Add salmon patty and top with 1 tbsp dill sauce. Top with other half of bun, and serve!
Use your favorite gluten-free buns for gluten-free.
To use fresh salmon, process 1 lb salmon (skin removed) in the food processor, then proceed with the recipe. The patties will take longer too cook than with canned salmon.