Preheat the oven to 375ºF / 190º C. Line a heavy sheet pan with parchment paper.
In a bowl whisk the labneh or yogurt, garlic, and salt.
In a sauté pan heat the olive oil over medium heat and sear the tomatoes cut-side down for 3-5 minutes (until caramelized and golden brown). Set aside.
Place one sheet of phyllo on the prepared sheet pan and brush to dab it with a coat of butter. Place the next phyllo sheets on top, one over the other, brushing them all with butter. Leave longer edges so you can fold them over the filling at the end.
Spoon the labneh or yogurt mixture in the center and spread it evenly. Place the caramelized tomatoes on top and scatter the olives over. Fold in the edges of the phyllo and brush it with the remaining butter.
Bake until the phyllo turns golden brown,about 25-30 minutes. Drizzle the center with olive oil and sprinkle with the chopped chives.