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Put the pines nut and garlic in a food processor and process to form a paste. Add the basil leaves, then pulse, scraping down the sides regularly.
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Add half of the oil, continue processing, then add the cheeses and the remaining oil and pulse to just combine. The pesto will remain bright green in colour unless you over-process it. Season with salt and freshly milled black pepper to taste.
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Store the pesto in a sterilised airtight jar in the refrigerator for 1 week, although it is best consumed within a few days of making.