Begin by preparing the remoulade sauce, mixing together mayonnaise, Dijon mustard, chopped capers, lemon juice, and finely diced pickles in a bowl.

Preheat your oven to 375°F and line a baking sheet with parchment paper. Place the salmon filet on the baking sheet, drizzle with neutral oil, and sprinkle with kosher salt and pepper. Bake for 15–20 minutes until opaque and flaky.

In a skillet, melt 1 tablespoon of unsalted butter over medium heat, add diced shallots, and cook until translucent, about 3–4 minutes. Toss in minced garlic and sauté for another minute until fragrant, then remove from heat.

In a large mixing bowl, combine flaked salmon, leftover mashed potatoes, sautéed shallots and garlic, seasoned breadcrumbs, Old Bay seasoning, and Dijon mustard. Mix gently until well incorporated.

Using your hands, shape the mixture into oval or round croquettes, about 2–3 inches in diameter, and place them on a lined baking sheet.

Heat a few tablespoons of neutral oil in a large skillet over medium-high heat. Fry the croquettes in batches for 2–3 minutes on each side or until golden brown and crispy. Use a slotted spoon to remove and transfer to a paper towel-lined plate.

Arrange the cooked croquettes on a serving platter, garnish with fresh parsley, and serve hot alongside remoulade sauce for dipping.