For the zaatar: Combine the sesame seeds, sumac, thyme and salt together in an airtight container.
For assembly and serving: Preheat the broiler. After it has risen, divide the full dough recipe in half, reserving one half to make Spinach Fatayer (keep the extra dough covered until ready to use). Cut the remaining half into 6 equal portions and roll each into a small ball shape. Preheat a large skillet over medium heat. Flatten one ball with the rolling pin, then prick lightly all over with a fork to prevent puffing.
Cook each dough round in the skillet over medium heat until toasted and browned in spots on the first side, 2 to 3 minutes, then remove from the heat (the dough will only be cooked on one side). Repeat with the remaining dough balls.
Meanwhile, mix 1/4 cup zaatar with 1/3 cup olive oil in a small bowl. Spread some of the mixture on the uncooked sides of the flatbreads, place on a baking sheet and broil until they are golden and crisp on top, about 2 minutes. Serve the manakeesh zaatar with sliced pickles, olives, tomatoes and mint.
Mix the flour, yeast, olive oil and salt in the bowl of a stand mixer fitted with the dough hook attachment. Add the warm water, a little at a time, until the dough starts to come together into one mass and forms around the hook. Increase the speed to high and continue kneading for 4 minutes.
Dust a work surface with flour and transfer the dough to it. Continue kneading by hand, then form the dough into a large ball, dust lightly with flour and place in a large bowl. Cover with a kitchen towel and let rise in a warm place for 1 hour.