Purée scapes, olive oil and juice in a blender or food processor until nearly smooth. (You can make a smooth paste if you prefer, but most people like a little texture in the pesto.)
Gently stir in the cheese or gingerly pulse the cheese into the mixture; take it easy as you mix in the cheese to avoid making the pesto gummy by over blending. Taste and then adjust juice and salt to taste.
Store in the refrigerator to use within 2 or 3 days. Freeze in airtight container for longer storage. When frozen, scape pesto holds its appealing green color better than the well-known basil-based pesto Genovese.