Preheat your oven to 350°F. While it heats, mince your garlic cloves and set aside, then zest your lemon and chop your fresh parsley. Pat the salmon fillets dry with paper towels and season both sides generously with salt and pepper. Place the salmon skin-side down on a baking sheet and transfer to the oven—this will cook for 15-20 minutes while you prepare everything else, so you're using your time efficiently.
While the salmon is in the oven, bring a large pot of salted water to a boil. Add the pappardelle and cook according to package directions until al dente (usually around 12-13 minutes). Reserve about 1/2 cup of pasta water before draining—this starchy liquid will help you adjust the sauce consistency later. Drain the pasta and set aside.
In a medium saucepan over medium heat, warm the olive oil and add your minced garlic. Cook for just 30-60 seconds until fragrant—don't let it brown or it will taste bitter. Immediately pour in the lemon juice and vegetable broth, stirring to combine, then let this simmer for about 2 minutes to allow the flavors to meld. This is where I like to add a pinch of salt to the broth to give the sauce more depth before the cream goes in.
Reduce the heat to low and pour in the cream, stirring gently. Add the freshly grated parmesan and lemon zest, stirring constantly for about 3 minutes until the cheese melts completely and the sauce becomes smooth and cohesive. The low heat is crucial here—if the temperature is too high, the cream can break. Taste and adjust seasoning with a pinch more salt or pepper if needed.
Remove the salmon from the oven—it should flake easily with a fork when done. Let it cool for a minute, then break it into bite-sized chunks, discarding any bones. Add the cooked pasta from Step 2 to the lemon cream sauce and gently toss to coat, adding splashes of reserved pasta water as needed to reach your desired consistency. The sauce should cling to the noodles without pooling at the bottom.
Gently fold the salmon chunks into the pasta and sauce, being careful not to break them up too much—you want distinct pieces of salmon in each bite. Divide among bowls or plates and garnish generously with the fresh parsley you chopped in Step 1. I always finish with a light crack of fresh pepper and a few extra shavings of parmesan for brightness and elegance.