In a small bowl, whisk together the olive oil, lemon juice, za'atar, minced garlic, salt, and pepper until well combined. Set aside.
In a large mixing bowl, combine the drained beans, halved green olives, quartered artichoke hearts, sliced red onion, and chopped parsley. Toss gently to mix.
Pour the prepared dressing over the bean mixture. Toss well to coat all ingredients evenly. Cover the bowl with plastic wrap and let it marinate at room temperature for at least 15 minutes, or refrigerate for up to 2 hours for deeper flavor.
Transfer the marinated salad to a round white serving bowl. Garnish with additional fresh parsley and a sprinkle of za'atar if desired. Serve chilled or at room temperature.