In a food processor, add basil and half of the olive oil. Pulse until coarsely chopped. Add ⅓ cup of oil and process until smooth. Season with salt.
If using immediately, add remaining ⅓ cup of oil.
If using later, transfer the pesto to an air-tight container and drizzle the remaining 1/3 cup of oil over the top. Cover and freeze for up to 3 months. Thaw when ready to serve.