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1
Stir the 1/4 cup warm water (first amount), 1 tablespoon sugar (first amount) and yeast together in a large bowl until the sugar is dissolved. Set aside until the mixture begins to bubble, about 10 minutes.
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2
Stir the all-purpose flour and bread flour together in a medium bowl. Stir the warm milk, 1/2 cup water, 1/2 cup plus 1 tablespoon sugar, butter and yolk mixture into the yeast mixture until well blended. Stir in the flour mixture, half at a time, and mix until you have a soft dough, 3 to 4 minutes. Cover the bowl with plastic wrap and place in a warm location. Let the dough rise, until roughly doubled in size, 2 to 3 hours.
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3
Preheat the oven to 350u00b0F.
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4
Turn the dough onto a floured cutting board. With a sharp knife, divide the dough into 15 roughly equal pieces. Roll a piece of dough out on a floured surface to a 4-inch circle. Place 1 1/2 tablespoons of desired filling into the center of the dough circle. Gather the edges of the dough over the filling, and twist them together to seal. Place the bun, seam side down, on a parchment paper-lined baking sheet. Repeat with the remaining dough.
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5
Brush all exposed surfaces of the buns with the beaten eggs. Bake until golden brown, 15 to 18 minutes. Serve warm.
