Place 1/4 of the salmon in a food processor. Add the dijon mustard, mayo, lemon juice, paprika, and cayenne pepper. Pulse to form a paste.
Dice the remaining 3/4 of the salmon fillets into small chunks, about ¼ inch thick.
In a bowl, combine the diced salmon, the salmon paste, 1/2 cup of the panko, scallions, yellow onion, 3/4 teaspoon Kosher salt, and 1/2 teaspoon ground black pepper. Do not overmix.
Line a baking sheet parchment paper and set aside. Divide the salmon mixture into 4 equal parts, and form 4 patties about 3/4 inch thick each. Place patties on the prepared baking sheet and cover with plastic wrap. Refrigerate the patties for at least 30 minutes so they hold their shape.
Make the lemon herb aioli: Combine all the aioli ingredients until smooth. Serve immediately or keep in the refrigerator for up to 1 day.
Place the remaining 1 1/2 cups panko bread crumbs in a shallow bowl. Press both sides of the patties on the panko bread crumbs.
Heat some olive oil on large non-stick skillet on medium heat. Cook the salmon patties for 4-5 minutes each side, until golden brown and cooked in the middle.
To build the burgers: Spread some aioli on the bun, add the arugula or lettuce, the patties, grilled onions, tomato, and avocado slices.