In the bowl of a stand mixer, combine warm milk, yeast, sugar, salt, butter, and eggs. Add in 5½ cups of flour. Using a dough hook, turn the mixer on to a low speed. Once the flour starts to incorporate into the dough, increase the speed to a medium range. Slowly add the remaining ½ cup of flour until the dough pulls away from the sides of the bowl. The dough mixture should be slightly sticky and soft. Add more or less flour until the dough reaches the desired consistency. The amount of flour you add in bread making is always an approximation and you should go by feel. Transfer the dough to a lightly greased mixing bowl. Cover with a towel and let rise 90 minutes. Lightly grease a baking sheet. Punch down the dough and form into 24 rolls. Place on the greased baking sheet in six rows of four. Cover and let rise 1 hour. Preheat oven to 375 degrees. Bake the rolls for 12 to 14 minutes, until lightly browned. Remove rolls from oven and brush with melted butter.