Whisk the flour, sugar, salt, and baking powder together in a large bowl. Add the leftover starter, yogurt, oil, and 1 tablespoon (15 ml) of water. Mix with your hands until a rough dough forms. The dough should feel soft but not sticky. Add more water or flour as needed to get the right texture. Cover with a damp kitchen towel and let rest for 1 hour.
Remove the dough onto a lightly floured work surface. Flatten into a rectangle, and then divide into 8 equal pieces, about 80 grams (23/4 oz) each. Cover with a damp towel.
Working with one piece at a time, roll the dough into a thin circle about 8 inches (20 cm). The exact shape does not need to be perfect—you’re looking for something slightly smaller than the width of your skillet. Note: Thinly rolled dough will get you soft, bendable flatbreads; thicker rolled dough will create puffy flatbreads.
Melt the butter in a small saucepan or in the microwave. Warm a large cast-iron skillet over medium-low heat.
Place the dough into the warm, dry pan and cook for 2 to 3 minutes on one side. When the dough puffs up and has a few bubbles on the surface, brush lightly with some of the melted butter and flip it over. Cook for 1 to 2 minutes on the other side. When finished, brush with more butter and transfer to a cutting board. Wrap in a towel to keep warm. Roll out the next piece of dough and cook the rest of the flatbreads.
These sourdough flatbreads are best enjoyed warm. You can also reheat them in a low oven, about 275°F (140°C), in a foil package. For crispy flatbreads, reheat directly on the center oven rack.
Flatbreads will keep fresh stacked, wrapped, and stored at room temperature for 1 to 2 days. Reheat as indicated above for best texture. To freeze, cover the flatbreads in plastic wrap and foil for up to 3 months.
TIP: After you’ve made this recipe, try spicing up the dough with different seasonings. Chopped herbs including rosemary and sage are always nice or try a light dusting of garlic powder and sesame seeds. Sometimes I’ll fold in a handful of chopped scallions, which gives the dough a mild onion flavor.