Bring a large pot of salted water to a boil and add the pasta, cooking according to package directions until al dente. While the pasta cooks, do your mise en place: roughly chop the garlic cloves, grate the parmesan cheese, and measure out the arugula, sun-dried tomatoes with their oil, cashews, and fresh lemon juice. This parallel prep work ensures everything is ready when you need it.

When the pasta is almost done, add the arugula, grated parmesan, chopped garlic, cashews, sun-dried tomatoes (with their oil), salt, and black pepper to a food processor. Pulse until the mixture is finely chopped and resembles breadcrumbs—you want some texture here, not a completely smooth paste. I prefer to pulse rather than fully blend because it keeps the pesto from becoming too warm and losing the bright arugula flavor.

Reserve about 1/2 cup of pasta cooking water, then drain the pasta in a colander. While the pasta drains, pour the extra virgin olive oil and the fresh lemon juice into the food processor with the pesto mixture and pulse until everything is well combined and smooth. The heat from the just-drained pasta will gently warm the pesto without cooking it, preserving that fresh arugula bite.

Transfer the drained pasta to a large bowl or back to the empty pot, then add the arugula pesto sauce. Toss gently to coat the pasta evenly. If the sauce seems too thick, add reserved pasta water a tablespoon at a time until you reach a silky consistency that lightly coats each strand. I like the sauce to coat the pasta lightly rather than clumping, so don't be shy with the water—the starch in pasta water is what helps the sauce cling beautifully.

Divide the pasta among serving bowls and taste for seasoning, adjusting salt and pepper as needed. Finish each bowl with an additional drizzle of extra virgin olive oil and a light dusting of freshly grated parmesan cheese.