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Place about 1/4 of the salmon in the bowl of a large food processor. Add mustard. Run processor until the mixture is pasty. Transfer to a bowl.
Place the rest of the salmon in the food processor, and pulse just a couple times until coarsely chopped into ¼-inch pieces (do not over process this second batch of salmon, it should not get too fine or pasty, it should still have some texture.) Transfer to the same bowl.
Now add the minced green onions, parsley, and spices (coriander, sumac, paprika, black pepper). Season with kosher salt. Mix well until the mixture is combined. Cover and chill in the fridge for about 1/2 hour.
While the salmon chills, prepare the toppings. Make the Greek Tzatziki Sauce according to this recipe. Prepare the arugula, sliced tomatoes, and the remaining toppings and buns to serve.
When ready, take salmon mixture out of the fridge. Divide into 4 equal parts. Form into 1-inch think patties.
Place bread crumbs on a plate. Place each patty in the bread crumbs plate and press to coat on one side, turn over and press on the other side to coat. Place the breaded salmon patties on a sheet pan lined with parchment paper.
Cook salmon patties. Heat about 3 tbsp extra virgin olive oil over medium-high heat until shimmering but not smoking. Lower each of the patties carefully and cook, for 2 to 4 minutes, turning over once, until lightly browned on both sides and medium-rare within), (adjust heat as necessary during cooking to keep things sizzling and cooking well but without scorching the bread crumbs.) (minimum internal temp should be 115 to 120°F on an instant-read thermometer for medium-rare.)
Set cooked salmon burgers onto paper towel to drain any excess oil; sprinkle lightly with Kosher salt if you like. Add a squeeze of fresh lemon juice on top.
Assemble in prepared buns. Spread the buns with a bit of tzatziki sauce. Add the salmon, then layer on the arugula, tomato and onion slices…enjoy!