Place milk in a small saucepan and bring it just to a boil. Immediately remove from heat and stir in sugar, butter, and salt. Let cool to lukewarm. (You don't want it hotter than 115 degrees.)
Mix together warm water and yeast. I do this right in the glass measuring cup that I measure the water in. Let sit a few minutes.
Pour yeast mixture into the mixing bowl for your electric mixer. Add milk mixture, eggs, and 2 cups of flour. Beat with paddle attachment until mixed.
Beat in remaining 2 1/2 cups flour gradually. There is a chance you will need a little less than 4 1/2 cups of flour.
Next knead the dough. You can use the dough hook and the electric mixer. Beat with speed set to 2 for about 7 minutes.Or you can knead the dough on a lightly floured surface for about 8 to 10 minutes. I like to use the dough hook for about 5 minutes and then knead by hand for a few minutes.
Place dough in a buttered bowl. Turn the dough ball so it gets greased with butter on all sides. Cover bowl with a kitchen towel or plastic wrap and set in a warm place to rise for 1 hour.
Punch dough down. Divide dough into balls of about 2 to 3 tablespoons each. Place in a greased 9x13-inch pan. I do 5 rows with 4 in each roll. Cover and let rise 1 hour.
About 10 minutes before rolls are ready to bake, preheat oven to 375 degrees.
Bake for 20 to 25 minutes, or until golden brown on top. Brush tops of rolls with butter and serve.