In the bowl of a standing mixer, whisk together the water, yeast, and sugar. Let rest until foamy -- about 5 minutes. (No rest is necessary if you know your yeast is viable.) Then add the milk, milk powder, shortening, salt, and half of the flour. Attach the dough hook and mix, at low speed, just until the flour is moistened -- about 30 seconds. Add the remaining flour. Starting at low speed and gradually increasing to medium speed, knead the dough until it is smooth, elastic, and not sticky to the touch -- about 8 minutes.
Form the dough into a ball, and then place it in a large, greased bowl. Flip the dough to grease its other side. Cover the bowl with cling film or a damp tea towel, and let the dough rise in a warm place until doubled in volume -- 90 minutes to 2 hours.
Gently punch down the dough to deflate it. Then cut the dough into 12 equal pieces. Form each piece into a tight ball. Then flatten one ball, and, while firmly poking your fingers into the dough, press it into a 5-inch-long oval or rectangle. Starting at a long end, roll the dough into a tight "cigar." Pinch the seam to seal it. Then place the cigar, seam-side down, on a parchment-lined baking sheet. Repeat for the remaining segments of dough, spacing them about 1 inch apart on the baking sheet. Cover loosely with greased cling film or a damp tea towel. Let rise in a warm spot until doubled in volume -- 30-45 minutes. Meanwhile, center the oven rack and preheat the oven to 400°F.
Brush the top of the buns with the egg wash. Bake until golden brown on the top -- 15 to 20 minutes. While the buns are still hot, brush their tops with the melted butter. Cool completely before slicing.