Yield: Yields 6 flatbreads.
Serve this Mediterranean-inspired flatbread with a seafood stew or grilled fish kebabs.
Let the dough rest in the mixer bowl for 5 minutes and then turn the mixer to medium-high speed and mix for 3 minutes more, as the dough vigorously slaps against the sides of the bowl.
Lightly oil a large bowl. Transfer the dough to the bowl and turn the dough to coat it with the oil. Cover with a damp cloth or plastic wrap and let the dough rise in a warm place until doubled in size, 1 to 1-1/2 hours.
Using a vegetable peeler, peel four 1×4-inch strips of orange zest, avoiding as much of the white pith as possible. Juice the orange and reserve 1/4 cup of the juice.
Put the orange zest in an 8-inch skillet and cover with the olive oil. Bring to a gentle simmer over medium-low heat and simmer until the edges of the peel start to frizzle, about 4 minutes total. Remove from the heat and let cool for 5 minutes. Remove the orange zest from the oil and drain on paper towels. Reserve the orange-infused oil.
While the oil is cooling, soak the coarsely ground fennel in the orange juice for 15 minutes. Drain and discard the orange juice (or use to make vinaigrette with some of the orange-infused olive oil). Finely chop the strips of zest and, in a small bowl, combine with the olives and soaked fennel. In another small bowl, mix the sea salt with the fennel powder.
With lightly floured hands, gently deflate the dough. Add the olive mixture to the top of the dough, and using a plastic bowl scraper, reach down to the bottom of the bowl and gently fold the dough onto itself 4 times, rotating the bowl with each fold, to incorporate the mixture. Turn the dough out onto a lightly floured surface, stretch slightly to form a log, and cut into 6 equal pieces. Shape each piece into a ball by gently stretching and tucking the dough underneath itself to form a “belly button” on the bottom. Gently roll in the palm of your hand to reshape into a uniform ball, then set each ball, belly button side down, on a well-floured baking sheet. Lightly brush each top with olive oil. Cover loosely with a towel or plastic wrap and let rise until doubled in size, about 1 hour.
Meanwhile, prepare a medium gas grill fire or a charcoal fire with a hot zone and a cool zone (an oven thermometer placed over the hot zone should register about 450°F). Brush the grill grates with a stiff brush, then wipe with a lightly oiled wad of paper towels.
On a lightly floured surface, roll out or press and stretch each piece of dough with your fingertips until about 1/4 inch thick and about 8 inches in diameter. Put the flatbreads on 2 lightly floured baking sheets and lightly brush the tops of the dough with the reserved orange-infused olive oil, being careful not to get oil on the baking sheet.
Put the flatbreads oiled side down on the grill (over the hot zone of the charcoal fire), cover, and cook until puffed and golden brown, 3 to 5 minutes. Flip the flatbreads and turn the burners of a gas grill down to low (or move the breads over the cool zone of the charcoal grill), and brush the grill-marked side with more of the oil. Cover and finish cooking until the bottoms are golden and the breads are cooked through, about 3 minutes more. Transfer the breads to a cutting board, drizzle with more of the oil, and sprinkle with the sea salt mixture—you may not use it all. Cut each into halves or wedges and serve warm.
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