Stir the yeast in the water and set aside for 5 minutes, or until it starts to bubble up.
Mix flour, salt, and sugar in a large bowl.
Gradually pour the yeast water and oil into the dry ingredients. Stir well to bind, then knead for 5 to 10 minutes. The dough should be smooth and elastic, and feel a bit like an earlobe.
Place the dough into a large bowl greased with olive oil. Place a damp tea towel over the dough and let rise in a warm place for 1 1/2 to 2 hours, or until doubled in size.
Punch down the dough. Divide the dough into four equal-sized pieces.
Place the dough back into the bowl and let rest for an extra 30 minutes.
Preheat oven to 450F.
On a floured surface, roll each ball of dough into a disc about 10-inches or 25-cm in diameter.
Transfer the dough to a cookie sheet.
Mix the za'atar spice mixture and olive oil to make a paste. Spread evenly over the four dough discs.
Bake 20 minutes, or until the crust is baked and golden brown.