In the bowl of a food processor fitted with a metal blade, combine scapes, pine nuts, and lemon juice and zest, and season with salt. Process, scraping down sides halfway through with a flexible spatula, until scapes and nuts are broken down into small pieces, about 1 minute. Add cheese and process until incorporated, about 30 seconds. Add basil and pulse until finely minced, about ten 1-second pulses.
Transfer scape mixture to a medium bowl. While stirring continuously, slowly pour olive oil into scape mixture in a thin stream. Season with salt and pepper to taste.
Pesto can be used right away, or transferred to a jar or container, covered with a thin layer of olive oil, and sealed, then stored following the instructions below.
