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.
Divide the salmon mixture into 4 mounds. With damp hands, pat into 4-inch-wide, 3/4-inch-thick patties.
Spread the remaining 1 cup panko on a plate. Press both sides of the salmon patties in the panko. Preheat grill to medium heat. brush grates with olive oil. Add the patties 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. Serve the patties on the buns; top with tartar sauce and desired veggies.