Bring a large pot of salted water to a boil, then add the pasta and cook until just al dente, about 8-10 minutes. Drain and rinse under cold water to stop the cooking process, then shake off excess water and set aside.
While the pasta cooks, toast the nuts in a dry skillet over medium heat until fragrant and lightly golden, about 2-3 minutes. Let them cool slightly.
Add the basil leaves, garlic, toasted nuts, pesto, lemon juice, and grated cheese to a food processor or blender. Blend until smooth and creamy, stopping to scrape down the sides as needed. Taste and season with salt and pepper, adjusting as desired.
Transfer the cooled pasta to a large mixing bowl. Pour the pesto over the pasta and toss gently until every strand is evenly coated with the vibrant, herby sauce. The pasta should glisten and look well-dressed.
Serve immediately for a fresh, chewy texture or cover and refrigerate for up to 24 hours. If refrigerating, toss again before serving to redistribute the pesto and refresh the coating.
Enjoy the chilled pesto pasta salad straight from the fridge or at room temperature, savoring the bright flavors and satisfying crunch of the cooled pasta coated in herby pesto.