Set a medium skillet over medium heat. Add 1 tablespoon of olive oil and 1 tablespoon of butter. Once melted, add the diced onion and bell pepper. Sauté until they become golden and softened, about 7-9 minutes. Remove the skillet from the heat.
In a large mixing bowl, combine the flaked salmon, sautéed pepper and onion, Panko bread crumbs, beaten egg, mayonnaise, Worcestershire sauce, garlic salt, black pepper, and chopped parsley. Stir everything together until well mixed.
Form the salmon mixture into patties, using about a heaping tablespoon for each one. Mold them with your hands into 2-inch wide by ⅓ to ½-inch thick patties.
In a clean non-stick pan, heat the remaining 1 tablespoon of oil and 1 tablespoon of butter over medium heat. Once hot, add the salmon patties in a single layer. Sauté for 3 to 4 minutes on each side, or until golden brown and cooked through.
Carefully remove the finished patties and place them onto a paper-towel-lined plate. Repeat the cooking process with any remaining oil, butter, and patties.
Serve the salmon patties warm, garnished with fresh parsley for an extra touch of flavor.