How to Make It
Combine flour, kaak, bulgur, sugar, yeast, salt, and fennel seeds in the bowl of a heavy-duty stand mixer fitted with the dough hook attachment. Add 1/4 cup oil, and beat on low speed until combined. Add 1 1/2 cups warm water and beat until dough starts to come together, about 4 minutes. Increase speed to medium-low, and beat until dough comes together and forms a ball, about 2 minutes. Turn dough out onto a lightly floured work surface, and knead 2 minutes.
Place dough in a large glass or metal bowl coated with 2 tablespoons oil, and turn to coat dough. Cover with plastic wrap, and let rise in a warm place until dough has doubled in size, about 1 hour and 15 minutes.
Whisk together za’atar and 3/4 cup oil in a small bowl.
Spread 1 tablespoon oil on each of 2 rimmed baking sheets. Remove dough to a lightly floured work surface, and cut into 10 pieces (about 4 1/2 ounces each). Shape each piece into a 5-inch circle, and place 1 inch apart on prepared baking sheets. Spread 1 tablespoon za’atar mixture on each dough round. Cover with plastic wrap, and let stand at room temperature until slightly puffy, about 1 hour.
Place a pizza stone in oven, and preheat oven to 525°F (do not remove pizza stone while oven preheats).
Working with lightly oiled hands, press each dough round into a thin 7-inch circle. Place 3 thin dough rounds on 1 rimmed baking sheet. Cover with plastic wrap, and let stand 15 minutes. Cover remaining dough rounds.
Place baking sheet with dough rounds on preheated pizza stone, and bake at 525°F until tops and bottoms of flatbreads are evenly browned, 7 to 9 minutes. Remove flatbreads from baking sheet. Repeat with remaining dough rounds.