Add baby arugula and spinach to the food processor. Pulse about 3-5 times until the leaves are chopped up finely. Then add in pistachios and pulse again, about 2-3 times. These steps help ensure your texture is smooth.
Add in remaining ingredients and process on low. You may need to stop a few times to scrape down the edges with a rubber spatula. Continue to spin on low until smooth. This can take about 2-3 minutes.
Once desired texture is reached, transfer to an airtight container and store in the refrigerator for up to 1 week. Pesto can be stored in the freezer for up to 6 months.