Place walnuts, garlic, arugula, nutritional yeast, salt, black pepper, and lemon juice in the bowl of a food processor fitted with thte blade. Pulse for a few seconds until walnuts are roughly chopped. With the food processor running, slowly pour in olive oil. Continue to process until mixture is well combined. Taste for seasoning and adjust with additional salt, pepper, or nutritional yeast to your preference.
In a large bowl, combine pasta, zucchini, green peas, broccoli, and arugula pesto. Add 2 tablespoons of reserved pasta water to moisten the miixture. Add additional pasta water asdesired, 1 tablespoon at a time. Add additional arugula pesto as desired. Serve pasta chilled, at room temperature, or hot.