In a small bowl or saucepan, melt 8 tablespoons of butter; set aside to cool. In a large bowl, whisk together the butter, milk, sugar, and eggs. In the bowl of a stand mixer fitted with the dough hook, mix 4 ½ cups of flour, yeast and salt. With the mixer on low speed, add the milk mixture. Once the dough comes together, increase the speed to medium and mix until smooth and shiny, about 4-6 minutes. (If the dough is sticky after 3 minutes, add the remaining flour 2 tablespoons at a time). The final dough will still be sticker than a standard bread dough. Turn the dough onto a lightly floured work surface, shape into a ball, and place in a lightly greased bowl. Cover with plastic wrap and let rest in a warm place until the dough is doubled in size, about 1 hour.