Preheat the oven to 170C/340F and place the nuts on an oven tray. Roast hazelnuts for around 10 minutes or until fragrant.
Remove the hazelnuts to a bowl to cool, and put the pine nuts on the tray. Roast the pine nuts for 5 minutes or until lightly browned.
Remove the skins from the hazelnuts by rubbing them between slightly damp hands. The skins will flake off.
Blanch the basil leaves by dipping them in a saucepan or bowl of freshly boiled water. Remove immediately to a plate lined with paper towels and pat them completely dry.
Blend the blanched basil leaves, grated cheese, olive oil, garlic, lemon juice, zest, pine nuts, and skinned hazelnuts until you reach your desired consistency.
Season to taste with salt and pepper, and adjust the liquidity with more olive oil if needed.
Notes
Store in the fridge in an airtight container with plastic food wrap covering the surface. Use within 3-4 days. Freeze in the same way, use within 1 month.