Bring a pot of salted water to a boil. Add the arugula and basil to the boiling water and cook for 2 minutes. Drain the arugula and basil and refresh under cold water and then press out as much liquid as possible. Transfer to a food processor with the remaining ingredients and pulse until smooth. Transfer to a bowl, cover and press a piece of plastic wrap against the surface.
The pesto can be made up to a day ahead and kept tightly covered in the refrigerator. Stir the pesto and bring it to room temperature before using.
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