Bring a large pot of water to a rolling boil. Add the 12 oz spaghetti and cook until al dente according to package instructions. Before draining, reserve 1 cup of the pasta cooking water, then drain the pasta and set aside.

While the pasta is cooking, zest one lemon and set the zest aside. Cut both lemons into halves. Squeeze the juice from one half (this is ½ lemon) and set it aside for the salmon. Squeeze the juice from the remaining three halves (these equal 1½ lemons) and set that juice aside for the sauce.

Pat the 2 salmon fillets dry with paper towels and cut them into bite-sized pieces. Season the salmon pieces with the ½ teaspoon cracked black pepper.

Heat a large nonstick skillet over medium-high heat. Add 1 teaspoon butter and 1 tablespoon olive oil and let the butter melt and the oil heat until shimmering.

Add the salmon pieces in a single layer and sauté over high heat for about 2 minutes, until a light crust forms and the salmon is almost cooked through. Remove the salmon to a warmed plate, squeeze the reserved ½ lemon juice over it, tent with foil, and set aside.

Reduce the heat to medium. Pour 1 cup heavy cream into the same skillet, add the reserved lemon zest and the juice from the 1½ lemons, and bring the mixture to a gentle simmer. Cook for about 2 minutes until the sauce thickens slightly.

Stir ¼ teaspoon salt into the sauce. Add ¼ cup of the reserved pasta cooking water to the skillet and simmer briefly to combine and loosen the sauce.

Add the drained spaghetti to the skillet and gently toss or stir to coat the pasta with the sauce. Add more reserved pasta water a tablespoon at a time if you need a thinner sauce or to help the sauce cling to the pasta.

Gently fold the cooked salmon into the pasta and sauce. Sprinkle with 3 tablespoons coarsely chopped parsley and serve immediately.