- Dice 4 ounces salmon into quarter-inch pieces. Set aside. Cut remaining fish into chunks and transfer to food processor, adding mustard, mayonnaise, lemon juice and zest, shallots, garlic, and cayenne. Pulse until pureed.
- Add pureed salmon to bowl of diced salmon. Add scallions, 2 Tbs. panko, 1/2 tsp. salt, and black pepper to taste. Fold gently until just combined.
- Line baking sheet with parchment paper and coat with olive oil. Divide salmon mixture in 4 mounds and place on parchment paper. Form mounds into burger patties. Cover and refrigerate for 30 minutes.
- Place remaining panko on plate. Coat both sides of patties in panko. Heat olive oil in large nonstick or cast-iron skillet over medium-high heat. Add patties and cook until browned, 3 to 4 minutes, adjusting heat as needed. Turn and cook until other side is browned and patty centers spring back when pressed, 3 to 4 more minutes.
- Transfer patties to plate lined with paper towel; season with salt. Serve on brioche buns; top with butter lettuce, onion and tomato slices, and tartar sauce.
Beverage pairing: Chilled pale ale or Pinot Noir