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Melt the butter in a wide pan over medium-low heat. Add the shallots and cook, stirring frequently, until golden and caramelized, about 20 minutes. When the shallots start to brown, reduce the heat to low and add a splash of water if the pan looks too dry. Season with a pinch of salt.
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Place the pie dough onto a lightly floured surface. Use a ring cutter to cut out 6 circles, 6 inches in diameter. Place the cut-out discs onto a baking tray lined with parchment paper.
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Divide the caramelized shallot onto the center of each dough round. Top with crumbled goat cheese and a sprinkle of za’atar. Fan the fig rounds over the top. Fold the dough edges over the figs to form pleats. Return the galettes to the refrigerator and chill until the dough is firm again, 20-30 minutes.
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Preheat the oven to 400˚F. Brush the crusts with the Lee Kum Kee Pure Sesame Oil and sprinkle with sesame seeds. Bake the galettes until the crusts are golden and the fruit is bubbling, 20-30 minutes. Remove to a serving platter, drizzle with honey, and sprinkle with a little more za’atar. Serve warm or at room temperature.