Combine kalamata olives, green olives, capers, garlic, anchovy fillets, and parsley in a food processor.

Pulse in short bursts 8-10 times until the mixture is coarsely chopped but not pureed—you want texture.

Add olive oil, lemon juice, and black pepper, then pulse just 2-3 more times to combine.

Transfer to a bowl, cover, and refrigerate for at least 30 minutes before serving to allow flavors to meld together.