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In a large bowl, whisk together the water, sugar, and yeast. Let sit for 5 minutes for the yeast to start working.
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Add 3 cups of the flour, the salt, melted butter, buttermilk, and egg. Beat on low speed for 2 minutes, scraping the bowl as needed.
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Knead, in a stand mixer using a dough hook or by hand, for 2 to 3 minutes, until smooth and elastic, adding more flour as needed to form a soft dough that cleans the sides of the bowl. Knead the scallions into the dough. Place in a greased bowl, cover, and let rise for 30 to 40 minutes, until doubled.
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Divide the dough into eight equal pieces. Shape each into a ball, then roll into 6" to 8" rounds about 1/4" thick.
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Preheat a large skillet, preferably cast iron, over medium-low heat. Put 1 tablespoon of oil into the hot skillet and tilt to coat the bottom. Cook each round for 1 1/2 minutes on the first side, then flip and cook the second side until golden. Brush with melted butter before serving.
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Store any leftovers, well wrapped, at room temperature for several days. Freeze for longer storage.