Boil the pasta: Bring a large pot of salted water to a boil. Cook the pasta until just shy of al dente, 1–2 minutes less than the package time. Reserve 1 cup of pasta water, then drain.

Season the salmon: Pat the salmon dry. Season both sides with salt and black pepper. If using one large fillet, slice into two or three portions for easier handling.

Cook the salmon: Heat a large skillet over medium-high heat. Add olive oil and 1 tablespoon butter. Place salmon in the pan, skin-side down, and cook 3–4 minutes. Flip and cook 2–4 more minutes, until just cooked through. Remove to a plate and tent with foil.

Flake the salmon: Once cool enough to handle, gently flake the salmon into large pieces, discarding the skin if you prefer. Keep warm.

Sauté the aromatics: In the same skillet over medium heat, add 1 tablespoon butter. Stir in garlic and cook 30–45 seconds, just until fragrant. Do not brown.

Deglaze: Pour in the wine (or broth) and scrape up any browned bits. Let it bubble for 1–2 minutes to reduce slightly.

Build the sauce: Add the remaining 1 tablespoon butter, heavy cream, and milk. Stir and bring to a gentle simmer. Do not boil hard.

Add cheese: Reduce heat to low. Stir in Parmesan a handful at a time until melted and smooth. Season with salt, pepper, and a pinch of red pepper flakes if using. Add lemon zest and 1 teaspoon lemon juice; taste and add more juice if desired.

Toss with pasta: Add the drained pasta to the skillet. Toss to coat, loosening with splashes of reserved pasta water until the sauce is glossy and clings evenly.

Fold in salmon: Gently fold in the flaked salmon and parsley. Warm through for 1 minute. Taste and adjust seasoning. Serve immediately with extra Parmesan and a lemon wedge.