Bring a large pot of salted water to a boil. Boil the pasta according to the DeLallo package instructions, approximately 10-12 minutes. Drain the pasta and pour back in the pot.
While the pasta is cooking, chop the walnuts in a food processor. Pour the walnuts into a small bowl then add the roasted red peppers, fresh basil, and garlic to the food processor. Pulse until finely chopped.
Add the Parmesan cheese, chopped walnuts, olive oil, and 1/2 teaspoon salt to the food processor, Pulse to combine. Salt and pepper to taste.
Pour the pesto over the cooked and drained pasta and toss to coat. Serve warm.