Combine yeast, sugar, and ½ cup water in a bowl of a stand mixer. Let sit for 5-10 minutes, or until the yeast starts to foam or “bloom”. **if the yeast does not bloom, you may need to get fresher yeast**
Add remaining water, egg, honey, oil and salt, mixing on low to combine. Replace the paddle for the dough hook.
Add the za'atar, and flour, one cup at a time, mix on low using the dough hook. Knead the dough until smooth and no longer sticky, adding more flour as needed. Transfer to a clean, oiled bowl. Cover with a clean, damp towel, and let rise until doubled in size, about 1 hour.
Preheat the oven to 350F. Line a baking tray with parchment paper.
Punch down dough to remove any air bubbles, and transfer to a floured surface.
Cut into 2 halves and each half into 3-6 pieces, depending on the braid. Roll each piece into a rope, approximately 12 inches long. Cover with a damp cloth and let rest for 10-15 minutes.
Make the egg wash: whisk together egg and water. Brush with egg wash, and top with more za’atar.
Bake for 40 minutes, turning the tray halfway through and brushing with additional egg wash.