Get the water going: Set a large pot on the stove, fill it with water, and bring it to a boil over high heat.

Add the 1 teaspoon kosher salt to the water so the pasta is seasoned as it cooks.

Toast the walnuts: While the water heats, put a large skillet over medium heat and add the walnuts to the dry skillet.

Cook the walnuts for 3 to 4 minutes, stirring often, until they smell nutty and look a shade darker. Transfer them to a cutting board or plate so they do not keep cooking in the hot skillet.

Start the pasta: When the water reaches a full boil, add the spaghetti to the pot and stir well so the strands do not stick together.

Cook the spaghetti according to the package directions until it is tender but still has a little firmness in the center when you bite it.

Build the base: While the pasta cooks, put the olive oil and anchovy fillets into the same skillet and set it over medium-low heat.

Use a wooden spoon to mash the anchovies into the oil as they warm. Cook for 1 to 2 minutes, until the fillets mostly dissolve into the oil.

Add the sliced garlic and red pepper flakes to the skillet. Cook for 30 to 60 seconds, stirring, until the garlic smells fragrant and just starts to turn pale gold at the edges.

Roughly chop the toasted walnuts if they are not already chopped, then add them to the skillet and stir for about 30 seconds so they are coated in the anchovy oil.

Loosen the sauce: Scoop 1 cup of the starchy pasta cooking water out of the pot and set it beside the stove.

Pour 3/4 cup of the pasta water into the skillet and let it bubble gently for 1 to 2 minutes. The liquid should look slightly cloudy and lightly thickened, not watery.