Cook the pasta: Bring a large pot of salted water to a boil and cook the pasta according to package instructions. Drain and reserve about ½ cup of the pasta water.

Make the pesto: While the pasta cooks, combine the arugula, walnuts, olive oil, garlic, and Parmesan cheese in a food processor or blender. Pulse until a coarse pesto forms, scraping down the sides as needed. Season with salt and pepper to taste.

Assemble the dish: In a large bowl, toss the drained pasta with the arugula pesto and about ¼ cup of the reserved pasta water until well combined. Add the sun-dried tomatoes and gently toss again.

Serve: Divide the pasta among serving bowls and garnish with additional Parmesan cheese, freshly ground black pepper, and optional fresh basil leaves.