In a large bowl, stir together 1/4 cup warm water, 1 tablespoon sugar, and active dry yeast. Set aside for 10 minutes until bubbly.

In a medium bowl, stir together all-purpose flour and bread flour.

Add warm milk, 1/2 cup water, 1/2 cup plus 1 tablespoon sugar, softened butter, and beaten egg yolk mixture to the yeast mixture. Mix until well blended.

Gradually stir in the flour mixture until a soft dough forms, about 3-4 minutes.

Cover the bowl with plastic wrap and let rise in a warm place for 2-3 hours until doubled in size.

Preheat the oven to 350°F (175°C).

Turn the dough onto a floured cutting board.

Divide the dough into 15 equal pieces.

Roll each piece into a 4-inch circle.

Place 1 1/2 tablespoons of your choice of filling in the center of each circle.

Gather the edges of the dough over the filling and twist to seal.

Place the buns, seam side down, on a parchment-lined baking sheet.

Brush the exposed surfaces of the buns with beaten eggs.

Bake for 15-18 minutes, or until golden brown.

Serve warm.