In a food processor, combine basil, 1/4 cup of the walnuts, the garlic and lemon juice. While processing, slowly stream in olive oil until smooth. Transfer mixture to a bowl and stir in Pecorino Romano, salt and pepper. Set aside.
Using a vegetable peeler, create long strips of carrots and zucchini. Chop remaining 1/4 cup walnuts. Set aside.
Bring a pot of salted water to a boil. Add farfalle and cook 9 minutes. Drain and rinse under cold water until cool. Stir in pesto, carrot and zucchini strips, and remaining walnuts.