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Prepare the remoulade. Stir together the mayonnaise, mustard, dill, hot sauce, Worcestershire sauce, smoked paprika, garlic powder, Cajun seasoning, and optional lemon juice. Cover and refrigerate for at least 30 minutes.
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Pat the salmon dry and season it with ½ teaspoon of the Creole seasoning.
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Heat the olive oil in a skillet over medium heat. Add the salmon and cook for approximately 4 to 5 minutes per side, depending on its thickness, until the thickest part reaches 145°F. Transfer the salmon to a plate.
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Keep the remaining oil and flavorful browned bits in the skillet, removing anything scorched. Add the butter, onion, bell pepper, and celery. Sauté for 5 to 7 minutes, until softened and the excess moisture has cooked off.
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Add the garlic and cook for 30 seconds. Remove the skillet from the heat and allow the vegetables to cool.
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Once cooled, flake the salmon into chunky pieces in a large bowl.
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Add the cooled vegetables, mayonnaise, Worcestershire sauce, hot sauce, breadcrumbs, green onions, parsley, and remaining ½ teaspoon of Creole seasoning. Mix gently, leaving some larger flakes of salmon intact.
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Taste the mixture and adjust the salt, black pepper, Creole seasoning, or hot sauce as needed.
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Fold in the flour, followed by the beaten egg, until evenly combined. Do not taste the mixture after adding the raw flour and egg.
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Let the mixture rest for 10 minutes. If it is too loose to shape, add additional breadcrumbs 1 tablespoon at a time.
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Divide the mixture into approximately 8 croquettes. Shape each croquette to about ¾ inch thick.
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Arrange the croquettes on a tray and refrigerate for 30 minutes. Do not apply an outside coating.
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Wipe out the cooled skillet. Add approximately ¼ inch of fresh neutral oil and heat it over medium heat to approximately 350°F.
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Working in batches, fry the croquettes for approximately 3 to 4 minutes per side, until deeply golden and the centers reach 165°F. Adjust the heat as needed to prevent the outside from becoming too dark.
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Transfer the cooked croquettes to a wire rack to drain.
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Taste the chilled remoulade and adjust the seasoning if necessary. Serve it alongside the warm salmon croquettes.