In a large bowl, add the warm water. Sprinkle the yeast and about one teaspoon of the sugar. Let the mixture sit for about 5 minutes or until thick and foamy.
Add the egg, butter, warm milk, dry milk powder, the remaining sugar, and salt. Using a wooden spoon, stir until blended.
Add the flour and stir with a wooden spoon until a shaggy dough forms.
Turn the dough over on a flat working surface and knead for about 10 to 15 minutes or until smooth and elastic, lightly dusting hands with flour as needed to keep the dough from sticking.
Lightly oil a large bowl. Shape the dough into a ball and gently turn it over and gently swipe on the inside of the bowl to oil the top. Then flip and place in the bowl, oiled side up.
Cover with a clean towel and let the dough rise for 1 hour or until double in size.
Gently deflate the dough by punching down. Turn over on the working surface and gather into a ball. Cut the dough into halves and cut each half into 6 portions.
Using the palm of your hands, roll each dough into a smooth ball.
Arrange the balls in a single layer on a parchment-lined baking sheet, leaving about 2 inches of space in between.
Using a sharp knife or scissors, make a deep cut in each ball halfway, but not all the way through.
Loosely cover with a clean towel and let rest for about 10 minutes.
Meanwhile, preheat the oven to 350 F.
In a small bowl, make the egg wash by combining 1 egg and 1 tablespoon milk. Whisk until well-blended.
Brush the tops of the buns with the egg wash and bake for 20 to 25 minutes, or until lightly golden on top.