- In a blender or food processor, finely chopped the basil leaves, garlic, pine nuts and cheese. Reduce the speed and drizzle in the olive oil until the mixture is creamy and slightly grainy. Season with salt, to taste. Store the pesto in an airtight jar for 2 to 3 weeks in the refrigerator or 6 months in the freezer. Add a thin layer of olive oil on the surface of the pesto to prevent oxidation. On contact with air, it tends to darken. This is not a sign of deterioration of the pesto.