Start by bringing a large pot of salted water to a boil. Add the 12 ounces of dry pasta and cook according to package instructions until al dente. Reserve about ½ cup of the pasta cooking water before draining the pasta.
While the pasta is cooking, grab your food processor. Add the 4 cups of packed arugula, ¾ cup of walnuts, 3 cloves of garlic, ¾ cup of grated Parmesan cheese, 1 teaspoon of salt, and ½ teaspoon of pepper. Pulse the ingredients until they are coarsely chopped.
With the food processor running, slowly drizzle in the ¾ cup of olive oil until the pesto reaches a smooth and creamy consistency. You might need to scrape down the sides to ensure everything is well combined.
In a large mixing bowl, toss the drained pasta with the pesto. If the mixture seems too thick, add a little of the reserved pasta cooking water until you achieve your desired consistency.
Serve the Arugula Walnut Pesto Pasta warm, garnished with extra grated Parmesan cheese and a sprinkle of freshly ground black pepper. Enjoy this delicious dish with your favorite side salad or crusty bread.