The lemon really brightens up the sauce.
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 1 pound 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 1 1/2 pounds salmon fillets dry with paper towels and place on the baking sheet. Drizzle with 1 teaspoon olive oil and rub the oil all over. Season all over with 3/4 teaspoon kosher salt and 1/4 teaspoon 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 (it will continue to cook as it rests). 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 2 tablespoons unsalted butter in the now-empty pot over medium heat. Add 1 thinly sliced medium shallot, 4 minced garlic cloves, and 1/2 teaspoon of the kosher salt. Cook, stirring occasionally, until the shallot is softened, about 2 minutes.
Stir in 1 1/2 cups heavy cream, 2 teaspoons 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, 5 ounces baby spinach, and 1/4 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 1 medium lemon and 2 tablespoons 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.