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PdfIn a large bowl, whisk together the yeast and warm water. Let this sit for 5 minutes until it begins to swell and get cloudy. Add the flour, yogurt, salt, and sugar and mix into a shaggy dough with your hands. Knead the dough in the bowl for 3 to 5 minutes, letting it smooth out into a ball. Cover and let rest for 30 minutes.
Transfer to a lightly floured surface, knead for another 2 minutes, and shape into a smooth, tight ball. Use a bench scraper to cut the dough into eight equal pieces. Loosely cover with plastic wrap and let these pieces rest for another 20 to 30 minutes.
Position a rack in the center of the oven and set the broiler to high.
Dust the pieces with a bit more flour and roll them out into thin flatbreads, about ¼ inch thick. Transfer the pieces to a large sheet pan and drizzle each side with olive oil. Rub oil all over the flatbreads to ensure they are evenly coated.
Broil until puffed up and golden, 2 to 3 minutes. Flip the flatbreads and repeat. Broilers are finicky, so the first time you make this recipe, keep an eye on them, as the times may vary.