In a small mixing bowl, combine the olive oil, tahini, za’atar, lime juice, salt, preserve lemons. Set aside.
Set aside a few sprigs of dill and about 1/4 cup of feta to garnish. In a large mixing bowl, combine the tomato, cucumber, parsley, dill, capers, red onion, dates, and feta cheese. Drizzle the dressing over the salad and toss until just combined. Garnish with remaining feta cheese and dill.
For the board:
Arrange on a large board or platter the salad, in the center, with the dressing on the side.
Lay down the pita bread, cut into wedges, or pita chips, around the outside, with pita chips on the other side, and serve!