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1
Stir together warm water and sugar in a measuring cup, then sprinkle yeast over mixture and let stand until foamy, about 10 minutes. (If yeast doesn't foam, discard and start over with new yeast.)
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2
Stir together flour (3 3/4 cups), salt, and baking powder in a large bowl. Stir together yogurt, egg, and oil in a small bowl. Make a well in center of flour mixture and add yeast mixture and yogurt mixture, then stir in flour mixture gradually with a wooden spoon until dough just comes together.
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3
Knead dough on a lightly floured surface with floured hands, lightly reflouring work surface and your hands when dough becomes too sticky, using no more than 1/4 cup flour, until dough is smooth, soft, and elastic, about 10 minutes. Transfer dough to a lightly oiled large bowl and cover bowl with plastic wrap. Let dough rise in a draft-free place at warm room temperature until doubled in bulk, 1 1/2 to 2 1/2 hours.
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4
Put oven rack with pizza stone in lower third of oven and preheat oven to 450F. (Heating pizza stone will take about 1 hour.)
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5
Coarsely grate onion on largest holes of a box grater and drain well in a sieve. Cook onion and sesame seeds in oil in a 10-inch heavy skillet over moderate heat, stirring occasionally, until onion is just beginning to turn golden, about 12 minutes. Transfer to a bowl and cool to room temperature.
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6
Turn dough out onto a lightly floured surface without punching down. Cut dough into 2 pieces and transfer 1 piece to parchment-lined pizza peel or baking sheet. (Keep remaining piece of dough covered with plastic wrap.) Flatten dough with lightly oiled fingertips, patting and gently stretching into an 11- to 12-inch round.
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7
Spread half of onion mixture over round, then poke holes through dough all over with skewer.
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8
Slide bread, along with parchment, onto pizza stone. Bake until golden brown, 10 to 12 minutes. Remove bread from oven by sliding peel under parchment. Transfer bread to a rack and discard parchment.
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9
While first flatbread is baking, make another bread on another sheet of parchment, then bake in same manner. Serve flatbreads warm.
