In the bowl of your stand mixer fitted with the paddle attachment combine 2 cups flour, sugar, undissolved yeast and salt. Mix on low until combined.
heat the milk, water, and 1/4 cup butter in 30 seconds increments until very warm to the touch (120°F to 130°F).
Pour the milk mixture into the flour mixture. Mix on medium speed for 2 minutes.
Add in the egg and 1/2 cup flour and mix for 2 minutes at high speed. Stir in enough remaining flour to make a soft dough. Dough should form a ball and be slightly sticky. Knead on a lightly floured surface until smooth and elastic, about 8 to 10 minutes, or alternately, you can do this step in your mixer with a dough hook.
Cover the dough with a clean towel and let it rest for 10 minutes.
Line a large baking sheet with parchment paper. Set aside.
Divide the dough in half. On a lightly floured surface, roll each half to a 12-inch square, about 1/4-inch thick. Using a knife or a pizza cutter cut the dough into 6 (12 x 2- inch) strips. Then cut each strip into thirds (4 x 2-inch rectangles).
Melt the remaining 1/4 cup butter. Brush each rectangle with butter.
Crease each rectangle slightly off center with dull edge of knife and fold at crease, so it’s not quite folded in half.
Place the rolls onto the prepared baking sheet, short folded side facing down. Cover and place in a warm, draft-free place. Allow to rise for 30 minutes, or until doubled in size.
Preheat oven to 375°F.
Bake for 15-18 minutes, or until golden brown.
Serve warm.