Preheat the oven to 300°F
Place the walnuts on a tray and toast them for about 5 minutes.
In your chopper or food processor, add the first 6 ingredients and give a few pulses to start combining them. Then add the olive oil. It should be a paste. If too loose, then add more basil and parmesan cheese. Taste for seasoning with salt and pepper.
Note: This will keep in the refrigerator for a week.