Pour the warm water directly into a large, sturdy mixing bowl. Add the yeast and sugar to the water. Let stand undisturbed for five minutes until frothy.
Whisk the olive oil, plain yogurt, egg, and salt into the yeast mixture. Ensure the wet mixture is completely smooth and very well combined.
Stir exactly two cups of flour into the bowl using a wooden spoon. Gradually add more flour until a soft, slightly shaggy dough finally forms.
Turn the dough out onto a lightly floured surface. Knead the dough gently for five minutes until it is smooth and slightly tacky.
Place the kneaded dough into a greased bowl. Cover it securely and let it rise in a warm place for one hour.
Punch down the risen dough and divide it evenly into eight individual pieces. Roll each piece tightly into a smooth ball.
Roll each dough ball out into a six-inch flat circle. Keep the overall thickness very even to ensure proper, uniform cooking.
Preheat a heavy cast-iron skillet over medium-high heat. Lightly grease the hot pan with a small amount of oil.
Cook each dough circle undisturbed for two to three minutes. Watch for large surface bubbles and deep golden-brown spots on the bottom.
Flip the bread carefully and cook for another two full minutes. Remove the bread and keep it covered with a thick kitchen towel.
Mix the melted butter and minced garlic together in a small bowl. Brush the warm garlic mixture generously over each piece of cooked flatbread.