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 to the boiling water and cook according to package directions, stirring occasionally to separate the noodles, for 1 minute less than al dente. Meanwhile, cook the salmon.

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

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

When the pasta is ready, reserve 1 cup of the pasta water. 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 ½ teaspoon of the kosher salt. Cook, stirring occasionally, until the shallot is softened, about 2 minutes.

Stir in heavy cream, Dijon mustard, and the remaining 1 teaspoon kosher salt, and bring to a simmer. Simmer until slightly thickened, about 2 minutes more.

Add the pasta, baby spinach, and ¼ cup of the pasta water. Cook over medium-high heat, tossing constantly, until the spinach is wilted and the sauce thickens slightly and coats the pasta, 1 to 2 minutes. Toss in more pasta water a few tablespoons at a time if needed if the pasta is dry.

Turn off the heat. Add the finely grated zest of lemon and lemon juice, and toss to combine. Taste and season with kosher salt and black pepper as needed. Transfer to a wide 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.