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To make the dough: Weigh your flour; or measure it by gently spooning it into a cup, then sweeping off any excess. Combine all the dough ingredients and mix and knead — by hand, mixer, or bread machine — until a soft, smooth dough forms.
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Transfer the dough to a lightly greased bowl, cover, and allow to rest for about 90 minutes, until puffy but not necessarily doubled in bulk.
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To make the filling: Heat the oil in a sauté pan set over medium heat.
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Add the onion and cook until translucent.
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Add the garlic and ground beef and cook for 5 to 10 minutes, breaking the meat up as it browns, until it's cooked through.
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Season the filling with salt, pepper, and parsley, remove it from the heat, and cool to room temperature.
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Stir in the cheese. The filling can be made ahead of time, then wrapped and stored in the refrigerator until ready to use.
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Divide the dough into 16 equal pieces; if you have a scale they'll weigh about 2 ounces each.
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Shape the pieces into balls, and place them on lightly greased or parchment-lined baking sheets, leaving about an inch between them.
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Cover the dough balls, and allow them to rest for about 15 minutes.
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Shape each ball into a flattened round about 5" in diameter, brush the surface with some of the egg/water wash, and place 2 tablespoons of filling onto the center of each round; our tablespoon cookie scoop works well here.
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Pull the dough over the filling, pinching two opposite edges together tightly, to seal in the filling; it should look like a dumpling.
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Place the buns on two lightly greased or parchment-lined baking sheets. Cover the buns, and allow them to rise for 1 hour, or until puffy.
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Towards the end of the rising time preheat the oven to 400°F.
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Brush the buns with the remaining egg wash. Bake the buns for 15 to 20 minutes, until golden brown. It's OK if some of the seams have come undone and the filling is visible; they can be prettier that way!
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Remove the buns from the oven and allow them to cool for 5 to 10 minutes before serving.
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Store any leftover buns in the refrigerator.