Drain salmon then remove and discard any bones or cartilage. Transfer salmon to a medium bowl and flake salmon into small chunks using a fork.
Add 1 egg, 2 tablespoons grated shallot, 1 tablespoon lemon juice, 1 tablespoon mayonnaise, 1 tablespoon chives, 1 tablespoon dill, 1 tablespoon parsley, 1 teaspoon Dijon, ¼ teaspoon each salt and pepper, and pinch cayenne to salmon and mix until thoroughly combined.
Using a ¼ cup measure, scoop level amount of salmon mixture and form into a patty 2½-inches in diameter and ½-inch thick; transfer to a plate and repeat with remaining mixture.
Heat a 12-inch nonstick skillet over medium-high. Add 1 tablespoon oil and heat just until shimmering. Place half of salmon patties in skillet and cook, without moving, until golden brown, 2–2½ minutes. Carefully flip patties and cook until second side is golden brown, 2–2½ minutes. Transfer patties to a wire rack.
Wipe out skillet with a paper towel and repeat cooking process with remaining tablespoon oil and salmon patties.
Serve as desired, we like to top them with tartar sauce.