Boil the potato chunks in salted water until very tender, 12–15 minutes.
Drain well, then mash the potatoes smooth with half the salt. Let cool 5 minutes.
Whisk flour, baking powder, garlic powder, and the remaining salt in a large bowl.
Stir yogurt and mashed potatoes into the dry mix. Add warm water a little at a time to form a soft dough.
Knead on a floured surface for 1–2 minutes until smooth. Cover and rest 10 minutes.
Divide dough into 6 balls. Roll each into a 6–7 inch round, dusting with flour as needed.
Heat a large skillet over medium heat. Brush with a thin film of olive oil.
Cook one flatbread until bubbles form and the bottom is golden, 1–2 minutes. Flip and cook another 1–2 minutes.
Lower heat. Sprinkle some mozzarella on the cooked bread, cover the pan, and melt 30–60 seconds. Repeat with remaining breads.
Brush hot breads with butter. Finish with scallions and black pepper. Slice and serve warm.