Boil salted water in a large pot, add pasta, and cook until al dente, about 8-10 minutes. Reserve 1 cup of pasta water before draining.

Pat the salmon dry, season with salt and pepper, then sauté in olive oil over medium heat for 3-4 minutes per side until golden brown. Remove from pan.

In the same pan, add diced onions and sauté until translucent, about 3 minutes. Add butter, minced garlic, and dried parsley, cooking briefly until fragrant.

Return about 20% of the cooked salmon back to the pan. Gradually stir in lukewarm milk and reserved pasta water, mixing thoroughly. Incorporate parmesan until melted.

Gently fold in the remaining pasta and salmon, adjusting sauce consistency with additional pasta water. Warm through on low heat.

Plate the pasta and garnish with lemon zest, an extra sprinkle of parmesan, and red pepper flakes. Serve immediately.