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To make the dough: Weigh your flour; or measure it by gently spooning it into a cup, then sweeping off any excess. In a large mixing bowl, mix and then knead all of the dough ingredients together until soft and smooth. Cover and let rise for 1 to 1 1/2 hours or until almost doubled.
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Preheat the oven to 375°F. Line a baking sheet with parchment.
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Divide the dough in half and shape into two balls. Cover the dough and let it rest on the counter for 10 minutes. After this rest, roll each ball into a 9" circle and transfer the circles to the prepared pan.
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Cover with greased plastic and let rise until puffy, about 30 minutes.
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To make the topping: When the breads have risen, brush the tops with the beaten egg and sprinkle with seeds. Slash the top of each loaf in a grid pattern, with the cuts spaced 1" apart.
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Bake for 20 to 25 minutes, until golden brown. Remove from the oven and serve warm.
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Wrap and store at room temperature for two days, or freeze for up to a month.
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To make the Baba Ghanoush: Preheat the oven to 375°F. Wash the eggplant and thoroughly char the outside on a grill or over an open flame on a gas stove. Transfer to a parchment-lined baking sheet and bake for 20 minutes, until soft.
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Toss the garlic cloves in a small baking dish with the olive oil and roast for 10 minutes, until soft. Remove from the oven, cool and peel the cloves, and save the olive oil.
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Peel the eggplant and put the flesh in the bowl of a food processor with the garlic cloves, reserved olive oil, tahini, lemon juice, and salt. Process until smooth, and refrigerate until ready to serve.
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Store Baba Ghanoush covered and refrigerated for up to a week.