In the bowl of a standing electric mixer, combine the yeast with 2 tablespoons of the water and let stand until moistened. Add the flour, olive oil, honey, 2 teaspoons of salt, and the remaining water. Fit the mixer with the dough hook and mix on medium-low until a firm, supple dough forms, 15 minutes. Turn the dough out onto a floured surface and cut into thirds; let stand for 15 minutes.

Preheat the oven to 325 degrees. Lightly coat the underside of three 12-by-15-inch rimmed sheet pans with vegetable oil. On a floured surface, roll out the dough to rectangles slightly larger than the sheet pans, a scant 1/8 inch thick; if the dough springs back, let rest for a few minutes before rolling again. Drape each rectangle over the underside of each sheet pan so it hangs over the edge.

Sprinkle each rectangle with water, then sprinkle with 1/2 teaspoon of kosher salt and 1 tablespoon each of the za'atar and sesame and poppy seeds (1 flavor per tray). Leave the dough whole or, using a pastry wheel, cut it into twelve 3-by-5-inch pieces.

If you have 3 racks in your oven, bake 1 pan of lavash on each rack for 40 minutes, until browned and crisp; shift the pans halfway through baking. If you have 2 racks, bake the lavash in shifts for 35 minutes per batch. Transfer the lavash to racks and let cool. Break the lavash as desired and serve.

Za'atar, a Middle Eastern mix of sesame seeds, herbs and sumac, is available at specialty shops and from penzeys.com.