Mix together the yeast, sugar and water in a small bowl and set aside for a few minutes to foam up while you measure and mix other ingredients.
In a larger bowl, mix together the flour and salt. Add the yeast mixture and oil then mix everything together and bring the dough together in a ball. If it's not all coming together, add a little more water.
Transfer the dough to a lightly floured surface and knead for around 3-5 minutes just to get the gluten going. Bring the dough into a ball. (Alternatively, you can mix and knead the dough with a stand mixer). Lightly oil a bowl and place the dough in the bowl, rolling in the oil, then cover with cling wrap/film and leave to double in size, around 90 minutes.
Once the dough has risen, knock it back gently and divide into 6 pieces (or 4 if you want larger-sized bread). Roll each into a ball and then cover with a damp cloth and leave to rise again, around 20-30 minutes. If you prefer, you can just leave them 10min or so to relax, then roll and leave to rise more later (see post above). As the dough is rising, mix together the oil and za-atar for the topping in a small bowl.
Roll each of the balls of dough into a flat, relatively thin circle (if you make six, they should be around 6in/15cm in diameter). Transfer them to parchment-lined baking sheets.
Spread the oil-za'atar mixture over the middle of each round of dough, leaving a rim around the edge of each without any of the mixture (around ⅔in/2cm). Leave the breads to rise slightly more, around 10 minutes or so as you pre-heat the oven to 430F/220C.
Once the oven has come to temperature, bake the breads for around 10 minutes until they are starting to turn golden brown around the edges and have a hollow sound when tapped. Allow to cool a few minutes before serving.