Arrange an oven rack 5 to 6 inches below the broiler element, then set the oven to broil. Line a rimmed baking sheet with aluminum foil.

Bring a large pot of heavily salted water to a boil. Add dried fettuccine or linguine and cook according to package directions for 1 minute less than al dente.

Pat salmon fillets dry with paper towels and place on the baking sheet. Drizzle with olive oil, rub it all over, and season with kosher salt and black pepper. Arrange skin-side down.

Broil salmon until almost cooked through or registers about 115?F in the thickest part, 4 to 8 minutes. Meanwhile, finish the pasta and sauce.

Reserve 1 cup of pasta water, then drain the pasta and leave in the strainer.

Melt unsalted butter in the now-empty pot over medium heat. Add thinly sliced shallot, minced garlic, and 1/2 teaspoon kosher salt. Cook until the shallot is softened, about 2 minutes.

Stir in heavy cream, Dijon mustard, and remaining kosher salt. Bring to a simmer and simmer until slightly thickened, about 2 minutes.

Add pasta, baby spinach, and 1/4 cup of the reserved pasta water. Cook over medium-high heat, tossing constantly, until spinach wilts and sauce thickens slightly, 1 to 2 minutes. Add more pasta water if needed.

Turn off the heat. Add finely grated lemon zest and lemon juice, then toss to combine. Taste and season with additional kosher salt and black pepper if needed.

Transfer to a serving platter. Break up the salmon into large chunks and place on the pasta, leaving the skin behind. Garnish with freshly ground black pepper if desired.