Salmon Preparation: Preheat your oven to 425˚F (218˚C). Line a rimmed baking sheet with parchment paper or a silicone liner. Place the salmon filet in the center of the sheet, skin-side-down. Drizzle the salmon with olive oil and season it with garlic salt and black pepper. Bake the salmon uncovered for 10 to 15 minutes, depending on the thickness of the filet, or just until it is cooked through. Upon removal from the oven, cover the salmon with foil and allow it to rest for 10 minutes. Proceed to flake the salmon with two forks, discarding the skin and any bones, then set aside to cool to room temperature.
Vegetable Sauté: In a medium skillet over medium heat, combine 1 tablespoon of olive oil and 1 tablespoon of butter. Add the diced onion and bell pepper to the skillet and sauté until they are golden and softened, approximately 7 to 9 minutes. Once done, remove the skillet from heat.
Patty Formation: In a large mixing bowl, combine the flaked salmon, sautéed pepper and onion, bread crumbs, beaten eggs, mayonnaise, Worcestershire sauce, garlic salt, black pepper, and chopped parsley. Stir the mixture to combine it thoroughly. Form the mixture into patties, using about a heaping tablespoonful for each. Mold the patties with your hands into patties approximately 2 inches wide and 1/3 to 1/2 inch thick.
Cooking the Patties: Heat a clean non-stick pan with 1 tablespoon of oil and 1 tablespoon of butter over medium heat. Once the pan is hot, add the salmon patties in a single layer. Sauté them for 3 to 4 minutes per side, or until they are golden brown and cooked through. If the patties brown too quickly, reduce the heat. Once cooked, transfer the patties to a paper-towel-lined plate. Repeat the process with the remaining oil, butter, and salmon patties.