In the bowl of stand mixer, add the milk and 1/2 tsp of granulated sugar. Whisk in the yeast. Cover bowl and set aside for 8-10 minutes. Yeast mixture should take on a foamy appearance with a fermented aroma.
Add the flour, salt, remaining sugar and eggs into bowl with yeast mixture
With the dough hook attached, mix the dough ingredients together at low speed until a shaggy dough forms. At this point, mix in the butter a little at a time until all of the butter has been mixed into the dough.
Increase mixer speed to medium high and knead the dough for 6 minutes. The resulting dough should be soft touch but not overly sticky.
Transfer dough to a lightly greased bowl, cover with plastic wrap and place in a warm area to rise until doubled in size, about 60-90 minutes.
Deflate risen dough. Let dough sit for 5 minutes and divide into (5) equal portions. Shape each portion of dough into even sized buns and transfer to a parchment paper lined baking sheet.
Lightly cover baking sheet with plastic wrap and let buns undergo a second rise for 30-45 minutes or until doubled in size.
Preheat oven to 350F. In a small dish, whisk together the egg and water to make egg wash. Use a pastry brush to apply egg wash over the surface of risen buns.
Bake the buns for 25-30 minutes or until a toothpick inserted into one of the buns comes out clean and the buns have taken on a rich golden brown color.
Rest buns on baking sheet for 5-6 minutes before transferring to a cooling rack to cool to room temperature.
Use cooled buns in your favorite recipes and enjoy!