Heat the milk to about 180 degrees, either on the stove or in the microwave.
Remove the milk from the heat and add the butter.
When the Thermometer reads 120, dissolve the yeast and 1 teaspoon of sugar in the hot milk.
Let sit for 10 minutes; while the yeast begins to bloom, or foam.
In the mixing bowl of a stand mixer, add the yeast/milk mixture, pinch of salt and one cup of flour.
Using the paddle attachment, combine all ingredients plus egg, and mix until well incorporated.
Add 2 cups of flour, one cup at a time, until well blended.
Scrape down the sides of the mixing bowl and mix any unmixed ingredients.
Replace the paddle attachment with the dough hook.
Add the remainder of the flour about a 1/2 cup at a time, and mix on low speed until the dough forms a ball and pulls away from the mixing bowl.
Continue to mix/knead the dough for 3 minutes, or until the dough texture is smooth.
Place melted butter in a large bowl and smear the inside of the bowl with the butter.
Place the dough on a floured surface, and with floured hands, form the dough into a ball.
Place the dough in the buttered bowl, and turn the dough in the bowl to butter the dough.
Cover the dough with a damp cloth, and place in a warm place and let the dough rise until it doubles in size, about an hour.
When the dough has doubled in size, turn it out onto a floured surface and using a flour dusted rolling pin, roll the dough out to 1/2 inch thick.
Fold the dough in half, and seal the seams with the rolling pin.
Cut 3 X 3 inch pieces to make the rolls.
Grease a cookie sheet, and place the rolls on the cookie sheet.
Let stand until doubled in size, about 15 - 30 minutes.
Bake rolls at 350 degrees for about 12 minutes or until rolls are lightly browned.
Remove from oven to a wire rack and let cool.
When rolls have cooled, brush with melted butter.