Cook pasta according to package directions until al dente. Reserve 1/2 cup of pasta water before draining.
Preheat oven to 400°F. Place salmon fillets on a baking sheet lined with parchment, drizzle with olive oil, and season with salt and pepper.
Bake salmon for 12–15 minutes, or until it flakes easily with a fork. Remove from oven and let it rest for a couple of minutes before breaking it into large chunks.
Meanwhile, in a large skillet, melt the butter over medium heat. Add the minced garlic and chili flakes and stir until fragrant, about 1 minute.
Pour in the white wine, let it bubble for 2 minutes, then reduce heat slightly and add the cream. Simmer for 3–4 minutes until slightly thickened.
Stir in the Parmesan, lemon juice, and zest. Toss in the drained pasta, adding reserved pasta water if needed to loosen the sauce.
Add the baked salmon chunks and gently fold them in. Sprinkle with fresh parsley and serve immediately.