Place ¾ cup of warm water and 1 teaspoon of honey in a measuring cup. Stir to ensure that the honey is fully dissolved.
Add the yeast and stir until it is well combined. Let it rest for 5 minutes. It will have a thick layer of bubbles on top.
In the same measuring cup, add ¼ cup olive oil and ½ cup milk. Give it a good stir. Set it aside.
Combine 3 ¼ cups all-purpose flour and 1 ¼ teaspoons kosher salt in a large bowl.
Add the yeast mixture and knead for 5 minutes, first mixing the dough until no flour remains and then turning it into a ball. In the end, it will be a very sticky dough, and that is normal.
Cover the dough with a clean kitchen towel and let it rest in a warm part of your kitchen for 20 minutes. It will get slightly larger in size.
Transfer the now-rested dough to a lightly floured surface.
To knead the dough, press it with the heel of your hand, then push it away, fold it back over, and rotate it 45 degrees. Repeat this process for 5 minutes or until the dough is smooth. If it's too sticky to work with, sprinkle in a bit more flour, 1 tablespoon at a time.
Shape the dough into a log and divide it into 10 equal pieces.
Roll each piece into a ball, dust it with flour, and transfer it onto a plate. Loosely cover the plate with a kitchen towel and let it rest for 20 minutes.
When you're ready to cook, heat a large (12-inch) nonstick or cast-iron skillet over high heat for 5 minutes. The pan needs to be very hot to keep the dough from sticking. To test, flick a few drops of water into the skillet. If they sizzle and disappear right away, it's ready.
While the pan heats up, roll out one dough ball into a 10-inch circle using a rolling pin and more flour as needed. As you roll, it might be tricky to keep a perfect circle, and that's totally fine. Just do your best.
Carefully transfer the rolled dough to the hot skillet. Cook for 10 seconds (you'll see bubbles forming), then flip. Cook for another 10 seconds, then flip again. Repeat for a total of 3-4 flips or until it looks fully cooked and has golden spots.
As soon as it's done, wrap the warm lavash in a clean kitchen towel and place it in a basket to keep warm. Continue adding each cooked piece to the basket, keeping them wrapped so they stay soft and warm while you finish the rest.
Repeat the same rolling and cooking process with the remaining dough balls.