Place the first 6 ingredients in a food processor; cover and pulse until chopped. Add the walnuts, lemon juice and zest; cover and process until blended. While processing, gradually add oil in a steady stream.
Serve desired amount of pesto with pasta. Transfer remaining pesto to ice cube trays. Cover and freeze up to 1 month.
To use frozen pesto: Thaw in the refrigerator for 3 hours. Serve with pasta.