Place the garlic scapes in the bowl of a food processor and pulse until they are broken down, about 30 seconds.
Add the nuts and pulse until they are combined with the garlic scapes, about 15 seconds. Scrape the sides of the bowl with a rubber scraper.
Turn the food processor to blend, and slowly drizzle in the olive oil. Turn it off the processor and scrape the sides again.
Add the lemon balm leaves, Parmesan cheese, salt, pepper, and process until it reaches the desired texture. Taste and adjust seasoning if needed.
Use immediately, store in the refrigerator, or freeze for later.
To refrigerate: Pour the pesto into glass jars, top with olive oil, cover and store in the refrigerator for about a week.
To freeze: Pack into freezer safe containers, label, and freeze for up to one year.
Makes about one cup of garlic scape lemon balm pesto.