Whisk the milk and yeast together in a large bowl (if using a standing mixer, use the mixer bowl). Let sit until the surface looks foamy, usually about 10 minutes.
In a separate small bowl, whisk together the egg, yogurt and melted butter. Add the yogurt mixture to the milk mixture in the big bowl and, using a handheld whisk, stir for 1 minute.
Add 2 cups of the flour, and whisk by hand until fully combined. Switch to a wooden spoon, and stir in the third cup of flour. The dough will be stiff; don’t give up! Add the last cup of flour, the baking powder and the salt, and stir them into the dough. If need be, knead the mixture in the bowl with your hand. It will be messy.
If using a stand mixer, mix with the dough hook attachment for 7-8 minutes on medium-high speed. If mixing by hand, scrape the dough onto a lightly floured surface and knead it for 9-12 minutes with lightly floured hands.
Grease the inside of a clean bowl lightly with olive oil. Form the dough into a ball, place it in the bowl, and cover with a barely damp kitchen towel. Let rise in a warm place until about doubled in size, about 30 minutes.
Divide the dough into 12 equal portions. Space them a few inches apart on a lightly floured surface. Cover again with kitchen towels, and let rise again until doubled in size, about 30 minutes.
While the dough rises, heat a pizza stone or 2 sheet pans in the oven to 500℉.
Roll or stretch the dough into very thin round or oval shapes. Bake the breads in small batches, 4-5 at a time, by carefully placing them directly on the hot stone or sheet pans. Bake for 2-3 minutes per side, or until slightly puffed, with a matte surface and lightly golden brown spots.
As you remove them from the oven (pro tip: use metal tongs!), wrap the breads immediately in the towel to keep them warm and prevent them from drying out. Serve as soon as all of the flatbreads have been baked, if you can wait that long.