Prepare the pasta - Bring a large pot of water to a boil. When water is boiling, add 1 tablespoon salt and dry pasta; stir to separate pasta. Cook pasta until al dente and drain; set aside.
Prepare the salmon - Adjust oven rack to upper-middle position and heat broiler. Line a baking sheet or pan with aluminum foil. Zest the lemon and set aside. Cut half of the lemon into thin slices and place on the lined baking sheet. Reserve the other lemon half to use later.
Season one side of the salmon liberally with salt and pepper, sprinkle with lemon zest, then rub with olive oil. Place the salmon on top of the lemon slices on the baking sheet. Broil until salmon is no longer translucent and is firm when pressed, about 10 minutes. Remove from broiler and sprinkle with lemon juice using the remaining half of lemon. Use a fork to flake the salmon into bite-sized pieces. The salmon skin will stick to foil and can be discarded.
Prepare the spinach pesto sauce - In a food processor, pulse the walnuts and garlic until chopped. Add two-thirds of the spinach (the remainder will be used later), oil, half (1/2 cup) of the Parmesan, and ¼ teaspoon each salt and pepper. Puree until smooth, scraping down the sides of the processor bowl as necessary.
In a large saucepan over medium high heat, pour in the heavy cream and simmer until reduced to 1/2 cup. Once reduced, add the spinach pesto, the reserved spinach, remaining parmesan and stir. Cook until cheese melts through and spinach wilts down.
To assemble - Transfer the cooked pasta to a large serving dish. Top with the spinach pesto sauce and salmon, and toss to combine. Serve with freshly grated parmesan.