If using a stand mixer, fit with the paddle attachment. Combine the water and dry milk in the mixing bowl and blend until dissolved. Add the yeast, sugar, salt, 1/3 cup of room temperature butter, egg and 2 cups of the flour. Blend on low speed until all ingredients are moist. Increase the speed to medium and mix for two minutes.
Add 2 more cups of flour and blend on low until ingredients are moist. Increase the speed to medium and mix for two more minutes. Add the remaining 1 1/2 cups of flour, 1/2 cup at a time and mix until combined. Once moistened, change to the dough hook and mix until the dough is smooth and starting to hold together. The dough will be loose and sticky and will not clean the sides of the bowl.
Scrape out the dough with a rubber spatula into a well oiled bowl or container. Cover the bowl with plastic wrap and place in a warm location free from drafts until the dough is doubled in size. (I use my microwave with the task light on.) This may take anywhere from 30 to 60 minutes.
Line two large rimmed baking sheets with parchment paper and set aside.
Gently deflate the dough by pressing down with your palm. Turn out the dough onto a well floured, clean work surface.
Cut the dough in half. Don’t knead the dough and try not to fold over. Cover the remaining dough until needed.
Working with half the dough, gently press or roll out to a little larger than an 8x18-inch rectangle, about 1/2-inch thick. Brush the dough with melted butter. Cut the dough in half lengthwise using a sharp knife or pizza cutter. Cut each half into 18 (2x4-inch) pieces. Pull one end of a piece of dough and stretch it out a little. Starting on the thinner end you pulled, roll up into spirals with the butter on the inside. (See video linked in notes) Place the rolls about 2-inches apart on the prepared pan with the thicker end piece facing down, all going in the same direction. At this point you can flash freeze the rolls for baking at a later time. See NOTES for freezing.
Lightly cover the rolls with a sprayed/greased piece of plastic wrap and place in a warm location until doubled in size, anywhere from 30 to 60 minutes. To check for proper rise, gently press an area around the bottom of one roll with a finger or knuckle. If the indentation springs back a little and does not fill in completely the rolls are ready to bake.
Bake at 375F for 15 to 20 minutes depending on the size of the rolls or until golden brown. Remove from the oven and immediately brush hot rolls with melted butter. Enjoy!