In a large pot over medium-high heat, boil water and cook the pasta al dente, according to package directions.
Heat the olive oil in a large skillet over medium-high heat, then add the salmon and cook until the salmon is cooked through, about 2-3 minutes per side.
Once cooked, transfer the salmon to a plate, chop into pieces, and set aside.
Pour the seafood stock into the skillet and use a wooden spoon to scrape up any browned bits at the bottom of the pan.
Add the butter and garlic and sauté for just 1 minute, until the garlic is soft and fragrant.
Pour in the cream and lemon juice, and stir regularly to create the sauce. Add a ladle of hot starchy pasta water if it starts to thicken too quickly.
Whisk in the flour and parmesan cheese and continue stirring until the cheese has melted and flour is dissolved into the sauce, which should be thicker now.
Add the pasta to the skillet and coat with the sauce.
Add back the salmon pieces and add the capers to the skillet; stir to combine.
Season with salt and pepper.
Garnish with parsley, a squeeze of lemon juice, and a light sprinkling of extra parmesan cheese just before serving.
Notes
Makes 4-5 servings (2 to 2.5 ounces of pasta per person)Storage: store in an airtight container in the refrigerator for up to three days. Make it dairy-free: Substitute your favorite dairy-free heavy cream for the cream, and your favorite dairy-free grated parmesan alternative for the parmesan cheese. Use vegan butter.