Chop the salmon. Pat the salmon fillet dry with paper towels and remove any pin bones. Using a sharp knife, finely chop the salmon into small ¼-inch pieces. Do not use a food processor — hand-chopping preserves the texture.
Mix the burger mixture. In a large bowl, combine the chopped salmon, egg, panko, Dijon mustard, mayonnaise, lemon juice, scallions, dill, garlic powder, smoked paprika, salt, and pepper. Gently fold with a fork until just combined. Do not overmix.
Form the patties. Divide the mixture into 4 equal portions and shape into patties about ¾-inch thick and 4 inches wide. Press a slight indent in the center of each patty with your thumb to prevent puffing.
Chill the patties. Place the patties on a parchment-lined plate and refrigerate for at least 20 minutes (or up to 24 hours). This step is essential for burgers that hold their shape.
Preheat the air fryer. Set your air fryer to 390°F (200°C) and preheat for 3 minutes. Lightly spray the basket with olive oil.
Air fry the salmon burgers. Place the chilled patties in the air fryer basket in a single layer, leaving space between each. Lightly mist the tops with olive oil spray. Cook for 8–10 minutes, flipping carefully halfway through, until the burgers are golden brown and reach an internal temperature of 145°F (63°C).
Rest and serve. Let the salmon burgers rest for 2 minutes before serving on toasted brioche buns with your favorite toppings.