Start by preparing your favorite remoulade sauce. Combine ingredients like mayonnaise, Dijon mustard, lemon juice, and seasonings in a bowl. Mix until smooth, adjusting flavors as needed, and refrigerate while preparing the croquettes.

Preheat your oven to 375°F. Place the fresh salmon fillet onto a parchment-lined baking sheet and drizzle it lightly with oil. Season with kosher salt and black pepper, then bake for 15-20 minutes until it flakes easily.

In a small skillet, melt unsalted butter over medium-low heat. Add chopped shallot and sauté for 3 minutes until translucent. Add minced garlic and cook for another minute without browning it.

In a large bowl, combine flaked salmon, leftover mashed potatoes, seasoned breadcrumbs, sautéed shallots, Old Bay seasoning, and Dijon mustard. Mix gently until combined. Shape into oval croquettes about 2-3 inches long.

Heat a generous amount of neutral oil in a skillet over medium-high heat until it reaches 375°F. Fry the croquettes for 2-3 minutes on each side until golden brown, about 6-8 minutes total. Drain on paper towels and sprinkle with kosher salt.

Plate the croquettes warm and garnish with parsley. Serve with chilled remoulade sauce for dipping.