Step 1

Heat butter over medium heat in a large heavy-bottomed frying pan. Add bell peppers and onion and cook, stirring occasionally until vegetables are soft, 7-8 minutes. Transfer to a plate and set aside.

Step 2

Cut three-quarters of the salmon into ¼-inch dice and place in a medium bowl. Cut remaining salmon into 1-inch pieces and add to a food processor with mustard, 1 tablespoon mayonnaise, the lemon juice, and lemon zest. Pulse ingredients into a paste, then transfer to bowl containing the 1/4-inch salmon pieces.

Step 3

Add 2 tablespoons of panko breadcrumbs, the cooked onion mixture, and Cajun seasoning; mix gently until combined. Form 4 equal-size salmon patties about 4 inches wide, using a 4-inch metal ring if you like for even shaping. Pour remaining panko onto a plate. Turn patties in panko to coat. Place on a plate or a sheet pan lined with parchment paper. Refrigerate patties at least 30 minutes or up to 1 hour.

Step 4

Meanwhile, prepare spicy mayo: Add ½ cup mayonnaise, the hot sauce, lime juice, and cayenne to a small bowl and mix until combined. Place in refrigerator until ready to serve (or up to 1 week ahead).

Step 5

Heat the large frying pan over medium-high heat. Add 1 tablespoon grapeseed oil. Transfer 2 patties to hot pan. Cook patties until browned on the bottom, 4-5 minutes. Flip patties and continue cooking until second side is browned, about 4 more minutes. Transfer to a plate and tent with foil. Wipe out pan with a paper towel to remove crumbs. Repeat to cook remaining patties with remaining oil.

Step 6

Spread spicy mayo on cut sides of hamburger buns. Arrange tomato slices, arugula, and pickles on each bottom bun. Top each with a salmon patty and the bun top, and then serve.