Sprinkle the packet of yeast into the warm water. Let it activate for about 10 minutes, until bubbly.
In the bowl of a stand mixer fitted with the dough hook, mix the milk, sugar, egg, salt and activated yeast. Melt 4 Tbsp. of butter in a microwave safe dish and mix it into the yeast mixture.
With the motor of the stand mixer running on low speed, slowly add the flour, one cup at a time. The dough will become soft and it will pull away from the sides of the bowl.
Place the dough into an oiled bowl and cover with a dish towel. Allow the dough to rise for about 90 minutes, until doubled in size.
Punch down the dough and dump it onto a work surface. Roll it into a rectangle shape that is 1/2 inch thick. Then, fold the short end to short end.
Cut 15 squares of dough and place them onto a parchment-lined baking sheet. Cover with a dish towel. Let the rolls rise for 40 minutes.
Preheat oven to 350F degrees. Bake the rolls for 17-20 minutes, until golden brown on top. Remove from oven. Melt the remaining 1 Tbsp. of butter and brush it onto the tops of the rolls.