Prepare the remoulade sauce by combining mayonnaise, Dijon mustard, capers, minced garlic, and lemon juice in a bowl. Whisk until smooth and set aside in the refrigerator to chill.

Preheat your oven to 375°F. Place the salmon fillet on a baking sheet. Drizzle with oil and season with salt and pepper. Bake for 15-20 minutes until cooked and flakey. Cool slightly then flake into a bowl.

In a pan over medium-low heat, melt unsalted butter and add the shallots, sweating for about 3 minutes. Add garlic and cook for an additional minute. Cool slightly before adding to salmon.

Combine flaked salmon with leftover mashed potatoes, breadcrumbs, sautéed shallots and garlic, Old Bay seasoning, and Dijon mustard. Gently mix until incorporated.

Form the mixture into oval-shaped croquettes, approximately 3 tablespoons each, and place on a lined baking sheet.

In a skillet, heat enough neutral oil to cover the bottom. Once hot, add croquettes to the skillet and fry for 2-3 minutes on each side until golden brown.

Transfer croquettes to a plate lined with paper towels to drain. Serve hot, garnished with parsley and with the remoulade sauce for dipping.