Step 1: Prepare the Lemon Aioli : In a small bowl, whisk together mayonnaise, minced garlic, lemon zest, lemon juice, Dijon mustard, salt, and pepper. Mix until smooth. Cover and refrigerate while preparing the burgers — this allows the flavors to meld.

Step 2: Prepare the Salmon Mixture : Finely chop half the salmon into small chunks and pulse the other half in a food processor until it forms a coarse paste. Combine both in a large bowl. Add melted butter, minced garlic, parsley, breadcrumbs, egg, Dijon mustard, lemon juice, paprika, salt, and black pepper. Mix gently until combined — avoid overmixing to keep the texture tender.

Step 3: Form the Patties : Divide the mixture into 4 equal portions and shape into patties about ¾ inch thick. Place them on a plate or tray, cover, and refrigerate for at least 15 minutes. This helps them firm up and hold together while cooking.

Step 4: Cook the Burgers : Heat olive oil or butter in a skillet over medium heat. Add the salmon patties and cook for 3–4 minutes per side, until golden brown and cooked through. The internal temperature should reach 145°F (63°C). Transfer to a plate and let rest for 2 minutes.

Step 5: Toast the Buns : Lightly butter the burger buns and toast them in the same skillet until golden and slightly crisp — about 1 minute.

Step 6: Assemble the Burgers : Spread a generous amount of lemon aioli on both sides of the bun. Layer lettuce, tomato, salmon patty, and onion rings if desired. Add a final drizzle of aioli and top with the remaining bun.