In a large bowl, combine the flaked salmon, breadcrumbs, mayonnaise, egg, Dijon mustard, lemon juice, green onions, garlic powder, Old Bay seasoning, salt, and pepper. Mix until well combined.
Form the mixture into patties, about 2-3 inches in diameter. You should get about 6-8 patties.
Heat the olive oil in a large skillet over medium heat. Once hot, add the salmon patties to the skillet, cooking in batches if necessary to avoid overcrowding.
Cook for about 4-5 minutes on each side, or until golden brown and crispy. Remove from the skillet and place on a paper towel-lined plate to drain excess oil.
For the remoulade, whisk together the mayonnaise, Dijon mustard, capers, lemon juice, hot sauce (if using), salt, and pepper in a small bowl until smooth.
Serve the salmon cakes warm with a generous dollop of tangy remoulade on the side.