Coarsely chop the leaves and tender stems of 2 medium bunches of fresh parsley until you have 2 packed cups. Repeat with 2 medium bunches of fresh cilantro until you have 2 packed cups.
Coarsely chop 1 bunch of fresh chives until you have 1/4 cup.
Add the chopped parsley, cilantro, and chives to a food processor fitted with the blade attachment or a blender.
Add 3 large or 4 small peeled garlic cloves, 1/4 cup plus 2 tablespoons extra-virgin olive oil, 3 tablespoons sherry vinegar, 2 teaspoons ground cumin, and 1 teaspoon kosher salt to the processor or blender.
Process the mixture (or use long pulses if using a blender), stopping and scraping down the sides of the bowl or blender jar as needed, until the garlic and herbs are very finely chopped and the texture is like pesto, 2 to 3 minutes.
Taste and season with more kosher salt as needed.