In a food processor, combine the salmon, egg yolk, lemon juice, salt, black pepper, and cayenne pepper. Blend for 10 seconds, or until all ingredients are well combined—be careful not to over-blend. Transfer the salmon mixture to a bowl and mix in the chopped parsley.
Wet both hands with water and shape the salmon mixture into 8 balls. Then, flatten each ball into patties.
Heat a skillet with cooking oil over medium heat. Transfer the salmon patties to the skillet and cook for 1 minute on each side, without interruption, until the patties are just cooked through. Transfer to a serving platter and serve warm with lemon wedges and sweet chili sauce.
