Add the yeast, 1 tablespoon of granulated sugar (reserve the remaining sugar for later, warm water and warm milk. Stir to combine and then set aside for 5-10 minutes, until the yeast is frothy and bubbly.
Add the butter, egg, salt, and 2 cups of flour. Use the paddle attachment to mix on low until combined. Scrape down the paddle and replace it with the dough hook attachment. Mix on low speed and add the remaining flour ¼ cup at a time until a soft dough forms and is only tacky to the touch, not sticky.
Increase the speed just slightly and let the mixer knead the dough for 6-8 minutes, until smooth and elastic.
Form the dough into a ball and place in a lightly oiled bowl. Cover and let rise in a warm place for an hour, until doubled in size.
Once risen, punch the dough down and split into two even portions. Form a ball with each and then roll out into a 12-inch circle. Use a large sharp knife or a pizza cutter to cut the circle into 12 equal sized wedges. Roll the wedges from the wide part to the narrow part to form the rolls. Place on a parchment lined baking sheet. Repeat with the second ball of dough.
Cover and let rise for 30-45 minutes. While the rolls are rising, preheat the oven to 350°F and melt 3 tablespoons of butter.
Bake for 12 minutes and brush with butter immediately after taking them out of the oven. These are best enjoyed fresh and are arguably even better when still warm out of the oven. Enjoy!