Trim the ends from 5 garlic scapes and coarsely chop.
Finely grate the zest of 1 medium lemon until you have 1 teaspoon; juice the lemon until you have 2 tablespoons.
Finely grate 1/2 ounce Parmesan cheese (about 1/4 packed cup).
Place the garlic scapes, 1/4 cup pistachios, and 1 packed cup baby spinach in the bowl of a food processor fitted with the blade attachment. Process until finely chopped, about 15 seconds.
Scrape down the sides of the bowl. Add the lemon juice and zest, Parmesan, and 1/2 teaspoon kosher salt. Process until a uniform paste has formed, scraping down the sides of the bowl halfway through, about 15 seconds total.
With the motor running, stream in 1/2 cup extra-virgin olive oil. Scrape down the sides of the bowl and continue blending as needed until the olive oil is fully emulsified and the pesto looks uniform, about 5 seconds.