Pour the water into a large mixing bowl. Sprinkle the yeast on the water then stir to combine. Mix in the 2 1/2 cups of flour, yogurt, egg, salt, and 3 TBSP of the oil thoroughly until a dough is formed.
Transfer dough to a well floured surface and knead for about 2 minutes (dough will be a little sticky). Form the dough into a ball and place into a large clean bowl. Drizzle 1 tsp of oil over the dough. Flip the dough around a couple times to coat in the oil. Loosely cover the bowl and set in a warm place to rise until doubled in size, about 1 hour.
Punch down the dough to deflate and separate into 4 equal size balls. Set the balls on a well floured surface and sprinkle a little extra flour on top of the dough balls to prevent drying out while you make the filling.
THE FILLING:
Heat the oil in a skillet over medium-high heat. When the oil is hot add the mushrooms and onion and cook, stirring occasionally, until mushrooms are browned and any liquid in the pan has evaporated, about 10 minutes.
Stir in the tomato paste, garlic, cumin, crushed red pepper, vinegar, and 1/2 tsp salt. Cook while stirring until heated through, about 2 minutes. Season with salt & pepper to taste then take off the heat and allow to cool for 10 minutes.
ASSEMBLING:
Roll out each of the dough balls into a 6-inch disk. Place an equal amount of mixture into the center of each of the dough disks. Bring up the sides of the dough disk up over the filling and pinch the dough together to seal. Gently roll the dough back into a 6-inch disk.
Heat a cast-iron skillet over medium-high heat until pan is very hot. When the pan is hot lay one of the dough disks into the pan and cook for 2 to 3 minutes, or until charred in a few spots then flip over and cook for 2 to 3 more minutes (you want to make sure the dough is cooked through). Transfer the bread to a plate and cook the remaining disks the same way.
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