For the Flatbread: Combine flour, salt, yeast, and sugar in the bowl of a stand mixer and whisk until combined. Add olive oil and the yogurt or milk and knead with dough hook at low speed until dough comes together into a smooth ball. Dough should stick slightly to bottom of bowl as it kneads (add slightly more yogurt or milk as necessary). Continue to knead for 5 minutes. Alternatively, form dough in a food processor by adding all ingredients and processing until the dough rides around the blade. Transfer the dough to a clean bowl, cover tightly with plastic wrap, and allow to rise at room temperature until roughly doubled in volume, about 2 hours.
Turn dough out onto floured work surface. Using a bench scraper or a knife, cut the dough into 6 equal pieces. Roll each piece into a ball, then place on a well-floured surface (leaving a few inches of space between each one) and cover with a floured cloth. Alternatively, place each ball of dough in an individual covered pint-size deli container. Allow dough to rise at room temperature until doubled in volume, about 2 hours.
