Combine the basil, garlic, and pine nuts in a food processor and pulse until coarsely chopped. Add the 1/2 cup of the oil and process until fully incorporated and smooth. Season with salt and pepper. If freezing, transfer to an air-tight container and drizzle remaining oil over the top. Freeze for up to 3 months.
Thaw and stir in cheese.
COOKS NOTE: If using immediately, add all the oil and pulse until smooth. Transfer the pesto to a large serving bowl and mix in the cheese.
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