Prepare the mixture: In a large bowl, combine the flaked salmon, mashed potatoes, green onions, parsley (if using), Dijon mustard, garlic powder, salt, and pepper. Stir everything together until well combined. Add the beaten egg and mix until the mixture comes together.

1. Form the fish cakes: Take a small amount of the mixture and shape it into a patty about 2-3 inches wide. Coat each patty in breadcrumbs, pressing gently to ensure the breadcrumbs stick. Repeat with the rest of the mixture.
2. Fry the fish cakes: Heat the olive oil in a large skillet over medium heat. Once the oil is hot, add the fish cakes to the skillet. Cook for 3-4 minutes per side or until golden brown and crispy. You may need to cook them in batches depending on the size of your skillet.
3. Drain and serve: Once the fish cakes are crispy and golden, transfer them to a plate lined with paper towels to drain excess oil. Serve immediately with lemon wedges and your choice of dipping sauce, such as tartar sauce or sour cream.