Pat the salmon dry, and season well with salt and cajun seasoning. Heat a large saucepan or skillet over medium heat. Preheat the oven to 425°F. Line a baking sheet with parchment paper.
Drizzle the salmon with 1 tablespoon of olive oil, and the juice of half a lemon. Season the salmon with 1-2 teaspoons of kosher salt (to taste) and 1-2 tablespoons of cajun seasoning (to taste). Place in the preheated oven and cook until the internal temperature reaches around 110°F-125°F for medium rare or your desired temperature. If you like your salmon more well done, cook it until it reaches 145°F.
Meanwhile, start the sauce on the stovetop. To the hot skillet, add the remaining 1 tablespoon of olive oil and 2 tablespoons of unsalted butter. Add in the onion, celery, and bell peppers with a pinch of salt. Cook until the peppers and onion are beginning to soften, about 3-4 minutes.
Meanwhile, bring a large pot of salted water to a boil for the pasta. Cook the pasta al dente, for 1-2 minutes under the package directions. It will continue cooking in the sauce. Reserve 1 cup of pasta water for later.
Add in 4 ounces of tomato paste, the zest of 1 lemon, the minced garlic, and 1-2 tablespoons more cajun seasoning to taste. Cook until the tomato paste deepens in color, about 3 minutes. Stir often to prevent burning.
Deglaze the pan with ¾ cup of white wine and ¾ cup of seafood stock, and stir to combine. Allow the mixture to simmer for 3-4 minutes to cook off the alcohol.
Reduce the heat to low, then stream in 1.5 cups of heavy cream, and stir to combine and warm through.
Begin adding in the parmesan cheese in small handfuls, stirring in between each addition until the cheese is completely melted before adding another handful.
Once all of the cheese is incorporated, remove the skillet from the heat and add in the pasta with a splash of pasta water and toss to combine. Next, add in the cooked salmon. Break the salmon into smaller pieces with a wooden spoon. Stir to combine and adjust seasonings to taste.
Serve with more parmesan cheese, lemon wedges, and fresh parsley. Enjoy!
Store leftovers in an airtight container in the fridge for up to 3 days. Reheat gently on the stove with more pasta water, broth, stock, or water to loosen the noodles. Do not freeze.