Fill a large pot with water for the pasta and bring it to a boil on the stove over high heat.
While you wait for the water to boil: assemble, measure, and chop the ingredients for the sauce: olive oil, garlic, chili pepper, walnuts, anchovies (or paste), and lemon juice. The sauce will come together quickly, so assembling the ingredients now is important.
When the water boils, generously salt and add the pasta.
Cook pasta according to package directions, minus 3 minutes for perfect al dente pasta.
The sauce will only take about 5 minutes, so start the sauce when there are 5 minutes left on the pasta cooking time.
In a large sauté pan, heat the olive oil over medium heat.
When the oil shimmers, add the walnuts and toast for about 2-3 minutes until they start to smell toasty. Add the garlic and chili pepper. Lower the heat to medium low or low to prevent the garlic from browning. Cook for about 1-2 minutes until the garlic becomes fragrant.
Add the anchovies (or paste).
Press down the chopped anchovies with the back of a wooden spoon. They will melt into the sauce, so keep pressing until they are fully incorporated. This should only take a minute or two. If you finish this step and your pasta is still cooking, remove your skillet from the heat and set aside. When you're ready to add the pasta water and then the pasta, place the sauté pan back on low to medium heat to warm it.
When the pasta is finished cooking, but BEFORE DRAINING, scoop out 1 cup of pasta water into a glass measuring cup. The pasta water will be added to the sauce to help bring the sauce together and create mouthwatering flavor. Drain the pasta and return it to the pot, drizzle with olive oil, and add a couple of tablespoons of butter (this will prevent the pasta from sticking together).
ANOTHER OPTION FOR THE PASTA: Use tongs to transfer pasta directly from the pot directly to the sauté pan. There should be enough water on the pasta make the sauce glossy, but save some of the pasta water in case you need to add a bit more. If you do it this way, be sure to turn off the heat on your stove first.
Back to the original method of draining the pasta: Before adding the pasta to the sauté pan, carefully stir the pasta water into the walnuts, anchovies, garlic, red chili peppers, and olive oil. The starch in the water will help the sauce coat the pasta and create a beautiful glossy sauce.
Using tongs, add the pasta to the saucepan , and toss with the sauce until the pasta is fully coated with the sauce. The pasta should look gorgeous and glossy.
Add the lemon juice, and toss a few more times over low heat.
Serve garnished with fresh parsley, and a generous helping of Parmesan cheese.
You can also drizzle a little bit of olive oil over the top because, well, why not?