In the bowl of a food processor, add the olives, capers, anchovy, garlic. Pulse several times until the olives are chopped but not pureed. Add the red pepper flakes, a pinch of black pepper, olive oil, balsamic vinegar, lemon zest, and lemon juice. Close the lid and pulse a few more times.
Transfer the olive mixture to a mason jar and place in the refrigerator for at least 2 weeks. If using fresh rosemary, remove it prior to serving.
