Dissolve yeast in warm water. Add 3 cups flour and salt. Stir in the remaining flour, 1/2 cup at a time, beating well after each addition.
Turn dough out on a lightly floured work surface. Knead until smooth, about 10 minutes. Grease a large bowl. Place dough in the bowl and turn to coat with oil. Cover and let rise in a warm place until doubled, about 1 hour.
Preheat the oven to 500 degrees F (260 degrees C).
Divide dough into 16 equal pieces and form into rounds. Roll into 1/4-inch-thick circles. Poke rounds with your fingers to create small indentations.
Mix za’atar and olive oil together in a small bowl. Spread over circles. Place on ungreased baking sheets.
Bake in the preheated oven until dough is golden brown, 5 to 6 minutes.