Toast the hazelnuts in a dry skillet over medium heat for about 5 minutes, or until golden and fragrant. Let them cool slightly and then rub with a towel to remove most of the skins.

In a food processor, combine the toasted hazelnuts, basil, Parmesan cheese, garlic, and lemon juice. Pulse until finely chopped.

With the food processor running, gradually add the olive oil to the mixture until smooth and creamy. Scrape down the sides as needed.

Season the pesto with salt and black pepper to taste. Process lightly to combine.

Transfer the pesto to a jar or container and cover with a thin layer of olive oil to prevent browning. Store in the refrigerator for up to a week.