Be sure to cut away any woody parts of the scape. Put the scapes and nuts (and basil, if using) into a food processor, pulsing until they start to look like a granular paste and clump around the blades.
Then add the lemon juice and Parmesan cheese, pulsing several times. Turn the food processor to low and add olive oil gradually as it becomes more paste-like, pausing to scrape down the sides of the bowl with a spatula.
Add fine sea salt and freshly ground black pepper, if using, to taste. Use immediately, or keep in a sealed container in the fridge for up to 7 days, or freeze in small, single-serving jam jars.
