Place the arugula, basil, mint, garlic, and cheese in the bowl of a food processor fitted with the steel blade. Pulse to combine, scraping down the sides as needed. Add the pine nuts and pulse several times.
With machine running, gradually add approximately ½-cup olive oil and puree until smooth. The amount of oil needed is up to each individual. If you prefer a thicker pesto, put less olive oil in the pesto. If you prefer a thinner pesto, add a little more olive oil.
Season with salt and pepper as needed.
Transfer pesto to a bowl. Can be made a day ahead and refrigerated. To freeze the pesto, place pesto into ice cube freezer trays. Freeze. Pop out the frozen pesto and put in freezer bags. You can pull out pesto as you need it in small quantities.