Bring a large pot of salted water to a boil. Cook the pasta according to the package directions until al dente. Reserve 1 cup of the pasta water, then drain.
While the pasta cooks, pat the salmon dry and season it with the salt and pepper.
Heat the olive oil in a large skillet over medium-high heat. Add the salmon and cook for 2 to 3 minutes per side, until lightly browned and nearly cooked through. Transfer to a plate.
Reduce the heat to medium. Melt the butter in the same skillet. Add the shallot and sun-dried tomatoes and cook until the shallot is softened. Add the garlic and cook for 30 seconds, until fragrant.
Add the tomato paste, Italian seasoning, red pepper flakes, and a pinch of salt and pepper. Stir to combine.
Reduce the heat to low and stir in the heavy cream and chicken broth. Add the Parmesan cheese a handful at a time, stirring until each addition melts before adding more.
Simmer gently for 2 to 3 minutes, stirring frequently, until the sauce begins to thicken. Keep the heat low so the cheese melts smoothly and the sauce stays creamy. Add the spinach and cook until wilted.
Return the cooked pasta to the skillet and toss to coat in the sauce. Add a splash of reserved pasta water if the sauce seems too thick.
Flake the salmon into large chunks with a fork and gently stir it into the pasta. Taste and adjust the seasoning if needed.
Serve with extra Parmesan cheese and fresh basil.
Notes
Keep the salmon chunky: Flake the salmon into large pieces so it does not fall apart when tossed with the pasta.Grate your own Parmesan: Freshly grated Parmesan melts more smoothly than pre-shredded cheese.Use full-fat heavy cream: Lower-fat dairy products can curdle or produce a thinner sauce.Save the pasta water: Reserve some pasta water before draining the pasta. It helps loosen the sauce without making it watery.Working with skin-on salmon: Sear it skin-side down first, then remove the skin before adding the salmon back to the pasta.Warm leftovers gently: Reheat over low heat with a splash of cream, milk, or broth to loosen the sauce. High heat can cause the sauce to separate and the salmon to dry out.Choose your pasta shape: Penne works well, but rigatoni, rotini, or farfalle are also good choices because they hold onto the creamy sauce.Store leftovers in the refrigerator for up to 3 days. The pasta tends to soak up some of the sauce during storage, so add a splash of chicken broth, cream, or milk when reheating to bring it back to a creamy consistency.