Add the olives, capers, parsley, garlic and lemon zest to the bowl of a food processor (see note). Pulse a few times in order to roughly chop the olives and parsley and to combine the rest of the ingredients.
Add in the miso paste, lemon juice and olive oil. Pulse a few more times, until everything is well-incorporated and the olives are finely chopped. Serve immediately or refrigerate.
Video
Notes
If you don't have a food processor, you can simply very finely chop the olives, capers and parsley. Add all the ingredients to a bowl and stir until well combined.