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 mis in the cheese.