Add the olives, olive oil, parsley, lemon zest, juice from half the lemon, rosemary, capers, garlic, pepper, and salt into a food processor. Pulse until you reach your desired consistency.
Taste and adjust the salt, pepper, and lemon juice, as desired.
Serve immediately or store in the fridge for 5-7 days. The flavors are even better after resting in the fridge for a day.