Combine green olives, anchovies, pine nuts, basil, parsley, capers, garlic, and lemon zest in a food processor. Pulse until coarsely chopped.

Add olive oil and Kosher salt, then blend until a smooth paste-like consistency forms. Taste and adjust seasoning, adding more salt as needed.

Use immediately or store in refrigerator, allow to sit at room temperature for 30 minutes before serving. Drizzle with extra olive oil and pine nuts.