Cut three-quarters of the salmon into 1/4-inch pieces. Put in a large bowl. Cut the rest of the salmon into chunks; transfer the chunks to a food processor along with the mustard, mayonnaise, lemon juice, lemon zest and cayenne. Pulse to make a paste. Add the pureed salmon mixture to the bowl with the diced salmon. Add the scallions, 2 tablespoons panko, 1/2 teaspoon salt, and black pepper to taste. Gently mix until just combined.
Line a baking sheet with parchment paper and brush with olive oil. Divide the salmon mixture into 4 mounds on the parchment paper. With damp hands, pat into 4-inch-wide, 3/4-inch-thick patties. Cover loosely with plastic wrap and refrigerate at least 30 minutes.
Preheat the broiler. Spread the remaining 1 cup panko on a plate. Press both sides of the salmon patties in the panko. Heat the olive oil in a large nonstick or cast-iron skillet over medium-high heat. Add the patties (in batches if necessary) and cook until browned on the bottom, 3 to 4 minutes, adjusting the heat if necessary. Turn and cook until the other side is browned and the patties feel springy in the center, 3 to 4 more minutes. Transfer to a paper towel-lined plate to drain; season with salt.
Meanwhile, arrange the buns, cut-side up, on a broiler pan and broil until toasted, 1 to 2 minutes. Serve the patties on the buns; top with tartar sauce and arugula.