Mix the Dough: In a large mixing bowl, combine the flour, yeast, and salt. Gradually add the warm water, lukewarm milk, and honey while stirring with a wooden spoon.
Knead the Dough: Once the dough becomes too difficult to mix with the spoon, transfer it to a clean, lightly floured surface. Lightly oil your hands with about 1/2 teaspoon of olive oil and gently knead the dough until it comes together (it will be sticky), which should take around 3 minutes.
Set Aside to Rise: Clean the mixing bowl or rinse and dry it thoroughly. Lightly coat the bottom and sides of the bowl with about 1 teaspoon of olive oil. Place the dough in the bowl, then drizzle about 1/2 teaspoon of olive oil over the top. Cover the bowl with a clean kitchen towel and let it rise in a warm spot for about 45 minutes.
Divide the Dough: Once risen, use oiled fingers to gently punch down the dough. Divide it into 12 equal-sized small balls (weighing about 1 1/2 ounces each can help with accuracy).
Prepare to Cook the Lavash: Place the dough portions on a floured surface and cover them with a clean cloth while you work on rolling and cooking each piece.
Roll the Dough: Take one ball of dough at a time, keeping the others covered. Place it on a floured work surface and lightly dust the top with flour. Flatten it with your hands, then use a rolling pin to roll it out as thinly as possible, achieving an approximately 8-inch diameter disc.
Cook the Lavash: Heat a large non-stick skillet over medium heat. Carefully place one lavash in the skillet and cook for about 30 to 40 seconds until bubbles appear and the bottom has some golden brown spots. Use a spatula to flip the lavash and cook for another 30 to 40 seconds until you see more bubbles and golden brown spots on the other side.
Cover and Repeat: Transfer the cooked lavash to a large tray and cover it with a clean towel to keep it warm and soft. Continue this process with the remaining dough until all the lavash is cooked. Serve warm or store for later.