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To make the dough: In a medium bowl, whisk together the flour, salt, and yeast. Add the water and mix until the liquid is absorbed and a sticky dough forms. Cover and set aside in a warm spot to rise for 1 1/2 to 2 hours, until the dough has nearly doubled in bulk.
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To make the sauce: In a medium skillet, heat the oil over medium heat. When it shimmers, add the onion and cook until translucent, about 5 minutes. Add the garlic and cook for 1 minute, until fragrant. Sprinkle with the salt, pepper flakes, cumin, and za’atar, stirring to coat. Add the tomatoes, stir, cover the pan, and reduce the heat to low. Simmer for 5 minutes, or until the tomatoes begin to break down. Uncover the pan and cook for 5 to 10 more minutes, until the sauce thickens. Remove from the heat, stir in the cilantro, taste, and adjust the seasoning as needed.
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To assemble: Line two baking sheets with parchment. Put three small puddles of olive oil, spaced 6” apart, on each pan (use a scant teaspoon of oil for each). Sprinkle 1/2 teaspoon sesame seeds into each puddle.
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Flour your hands and work surface. Deflate the dough, and turn it out of the bowl. Divide it into six pieces (they’ll weigh about 3 ounces each). Round up the balls of dough. Press each ball into a puddle, then turn it over and place on the pan. Let the dough balls rest for 20 minutes without touching them. While they're resting, preheat your oven to 350°F.
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Oil your hands and gently stretch each ball of dough to a 6” to 7” round, working from the center out. Leave the outside edge a little thicker, to form a border. Place 2 tablespoons of sauce atop the dough inside the border, pressing down in the center to form a cup. Brush the edges of the dough with water and sprinkle with the remaining sesame seeds.
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Bake the breads for 15 minutes. Remove the pans from the oven and crack an egg into the center of each round. Return to the oven and bake for 8 to 12 minutes more, until the eggs are just set and the yolks are slightly runny. Serve immediately.