Position a rack in the middle of the oven and preheat to 400 degrees.

Line a large, rimmed baking sheet with paper towels or a clean dish towel. Slice the tomatoes crosswise into circles about ¼-inch thick and place them on the towel-lined baking sheet. Sprinkle with salt on both sides to draw out moisture and cover with more towels to absorb the released juices while you prepare the crust.

In a medium bowl, stir together the cheese, labneh and za’atar until combined.

Cut a piece of parchment paper so that it will fit inside another large, rimmed baking sheet. Place the parchment on the counter and dust it with flour. Place the puff pastry on top of the parchment paper, sprinkle with more flour, and roll it out to a 12-by-14-inch rectangle. (Do not go beyond 12 inches on the short side or it will not fit on the sheet pan.) Transfer the parchment paper with the pastry to the second baking sheet.

With the tip of a sharp paring knife, score an approximately 1-inch border around the pastry, being careful not to cut through it.

Spoon the cheese mixture over the pastry, taking it up to, but not over, the scored border. Layer the tomatoes on top, letting them overlap slightly. Drizzle with the olive oil and sprinkle generously with sumac, to taste.

Bake for 20 to 25 minutes, or until the border puffs up and is nicely browned. Transfer to a wire rack and let cool for a few minutes or completely before slicing and serving.