Add 1/3 of the beet and turnip greens to the food processor. Pulse to chop. When the greens are chopped enough to allow room for more greens, add the same amount again and pulse to chop.
Add the last of the greens and the green garlic, as well as any other additions you're using, to your food processor. Drizzle in olive oil by going around the bowl of the food processor 4 times. Pulse until all ingredients are evenly sized and well mixed.
Add additional olive oil and continue to process until the pesto develops the consistency you prefer.
Use immediately, store in the refrigerator or freeze. This pesto can be used on pasta, as a sandwich spread, stirred into soup or in a multitude of other applications.