Mix yeast with warm water in a large mixing bowl and allow to stand until a creamy layer of foam appears, about 10 minutes. Whisk in 1/4 cup olive oil, then gradually stir in flour and 1/2 teaspoon kosher salt.

Transfer dough to a floured surface and knead until smooth and just a little bit sticky, about 10 to 12 minutes. Place dough into an oiled bowl, coat surface with oil, then cover and refrigerate overnight for the dough to double in size.

Coat a 9x13-inch baking sheet with 2 tablespoons olive oil. Place dough in the center, flatten into a thick disk, cover with plastic wrap, and allow to double in size for about 90 minutes.

Gently press and stretch dough to fill the baking sheet evenly. Create small indentations in the dough with your fingers. Brush the surface with remaining 2 tablespoons olive oil.

Stir za'atar and 3/4 teaspoon kosher salt in a small bowl and sprinkle it evenly over the flatbread. Let the dough rest, uncovered, for 30 minutes.

Preheat the oven to 375°F (190°C).