Before you begin mixing, flake the salmon into bite-sized pieces, removing any remaining bones or skin. Set aside in a bowl. Finely chop the parsley, thinly slice the green onions (white and light green parts only), mince the garlic, and grate the lemon zest fresh if you haven't already. I find that fresh lemon zest makes a noticeable difference compared to bottled, so it's worth the extra minute. Have all ingredients measured and prepped—this makes the mixing process quick and ensures even flavor distribution throughout the patties.
In a large mixing bowl, whisk together the egg yolk, mayonnaise, Dijon mustard, lemon zest, salt, pepper, and Old Bay seasoning. This creates the flavor foundation and binder for your patties. Stir until smooth and well combined. The mayonnaise acts as both a binder and adds richness, while the mustard and Old Bay provide savory depth that won't make the patties taste fishy.
Add the chopped parsley, sliced green onions, minced garlic, and the 1/4 cup panko bread crumbs to the binder mixture from Step 2, and stir to combine. The panko here adds texture and helps bind the mixture together. Gently fold in the flaked salmon from Step 1, using a spatula or wooden spoon to combine without breaking down the salmon flakes too much—you want some texture and visible pieces of salmon in the final patties. Don't overmix; a few gentle folds until everything is just incorporated is all you need.
Place the 3/4 cup panko for coating in a shallow dish. Scoop the salmon mixture into 8 equal portions (about 1/3 cup each) and shape each into a 3-inch patty about 3/4-inch thick. Working with one patty at a time, coat both sides generously with panko, pressing gently so the coating adheres. I like to coat one side, flip it carefully, then coat the other side and press gently to ensure the panko stays put during cooking. Arrange the coated patties on a clean plate or parchment paper until you're ready to cook them.
Heat 3 tablespoons of olive oil in a large skillet over medium-high heat until the oil is shimmering and just barely smoking at the edges (about 2-3 minutes). Carefully place 4 patties into the hot oil—they should sizzle immediately. Cook undisturbed for 2 minutes until the bottom is golden brown and crispy. Gently flip each patty and cook the other side for another 2 minutes until golden brown. The high heat creates a flavorful crust while keeping the inside moist. Transfer the cooked patties to a plate lined with paper towels to drain excess oil.
Add the remaining 3 tablespoons of oil to the skillet and let it heat for about 1-2 minutes until shimmering again. Cook the remaining 4 patties using the same method as Step 5: 2 minutes per side until golden brown on both sides. Transfer to the paper towel-lined plate with the first batch.
Arrange the warm salmon patties on a serving platter or individual plates. Serve immediately with lemon wedges on the side for squeezing over top. The patties are best enjoyed hot, when the exterior is still crispy and the inside is tender and flaky.