Stir 2¼ teaspoons of active dry yeast and ½ teaspoon of sugar into 1 cup of lukewarm water. Leave until foamy.
In a large bowl, mix 3 cups of unbleached all-purpose flour and 1 teaspoon of salt. Add 2 tablespoons of olive oil and the yeast mixture; knead until smooth and elastic. Cover and let rise for about 1½ hours.
Punch down the dough, divide into 8 balls and rest, covered, for 30 minutes. Meanwhile, preheat the oven to 400°F / 205°C with a baking sheet inside.
Mix 8 tablespoons of za'atar with ½ cup of olive oil. Flatten each ball into a 5in / 13cm disc and dimple with your fingertips.
Oil the hot baking sheet. Spread the discs with the za'atar oil and bake in batches for 7-8 minutes, until the bread is cooked through.