Add chopped garlic scapes into a food processor. Pulse several times, until the scapes break down. Scrape down the sides of the food processor as needed with a spatula.
Add the pumpkin seeds and pulse the mixture again until the seeds are coarsely chopped.
While the machine is running, slowly pour in the olive oil. Process on high speed for about 30 seconds.
Add the Parmesan cheese (unless you're going to freeze the mixture), and pulse until the cheese is combined into the mixture.
Add the lemon juice, and process until the mixture is combined. Season with salt and pepper to taste (add a little at a time and stir).
Store in an air-tight container with a thin layer of olive oil poured on top. The flavour will mellow after a day or two in the fridge. See notes for more storage tips.
Notes
For best results, chop scapes into small pieces before processing.
Add olive oil slowly for better texture and emulsification.
Taste and adjust seasoning as needed—garlic scapes can vary in intensity.
Store in the fridge for up to 1 week with a layer of olive oil on top, or freeze in cubes for longer storage. See the blog post for the full storage details.
Omit Parmesan if freezing, and stir it in after thawing for a smoother texture.
The pesto will have an intense garlicky flavour when it's fresh, but this mellows out a bit after a day or two in the fridge.
Warming the pesto also helps to mellow the flavour (adding it to very warm pasta, adding it to chicken before baking, etc.)
If you don't have a food processor, a powerful blender might work if you cut the scapes into smaller pieces.