Preheat your oven to 390°F. While it heats, finely mince the garlic cloves and chop the fresh dill and chives—having everything prepped before you start cooking ensures smooth timing. Place the salmon fillet on a baking tray, drizzle with olive oil, and season generously with salt and black pepper on both sides. Once the oven reaches temperature, place the salmon in to bake.
While the salmon bakes, bring a large pot of salted water to a boil and cook the pasta until just under al dente (about 1 minute before the package time suggests), then drain it while reserving 2/3 cup of pasta water for the sauce. Simultaneously, melt the butter in a large skillet over medium heat, then add the minced garlic and freshly ground black pepper, cooking for about 1 minute until fragrant. I like to use high-quality butter like Kerrygold here—it creates a noticeably richer, more luxurious sauce base that elevates the whole dish.
Pour the reserved 2/3 cup of pasta water into the pan with the garlic and butter, then bring it to a gentle simmer. Stir in the crème fraîche (which gives a better texture and creamier result than sour cream) and simmer for about 1 minute to incorporate it smoothly. Add the grated parmesan cheese and stir constantly until it's completely melted and the sauce becomes silky and cohesive. Finish by stirring in the lemon juice and capers for brightness and briny depth.
Check that the salmon has finished baking (it should be opaque and flake easily with a fork, around 10-12 minutes). Remove it from the oven and use two forks to gently break it into bite-sized pieces, discarding any bones or skin. Add the drained pasta from Step 2 to the creamy sauce and toss gently over medium heat for 1-2 minutes to allow the pasta to finish cooking in the sauce and absorb the flavors.
Divide the creamy salmon pasta between serving bowls or plates. Top each portion with the flaked salmon pieces and finish with a generous sprinkle of the fresh dill and chives. I find that adding the fresh herbs right before serving keeps them vibrant and adds a beautiful pop of color and freshness that really completes the dish.