Wash and gently pat dry the fresh basil leaves. Place the basil leaves in a food processor or blender. Pulse until finely chopped. Transfer the chopped basil into a clean, dry jar. Using a small spoon, cover the basil with a thin layer of olive oil to preserve it. Seal the jar tightly and store in the refrigerator. For best flavor, allow the basil to sit in the oil for at least 24 hours before using. Use as needed in your favorite recipes or as a fresh herb topping.