In a standing mixer, combine lukewarm water and yeast. Let it sit until dissolved for about 5 minutes.
Meanwhile, in a medium microwave-safe bowl, combine the milk with the butter pieces, sugar, and salt, and microwave for about a minute. Stir until everything is melted.
Allow the liquid to cool to 110℉/43℃ so you don't kill your yeast or curdle your eggs. Then, dump it into the yeast mixture.
Whisk an egg into the mixture.
Mix for 2 minutes at medium speed. Add about 3½ cups of flour and continue mixing the dough.
Add in enough flour as needed to make a soft dough. Err on the side of caution, less flour is better than more.
Turn dough on a lightly floured surface and knead for 3-4 minutes or more if you want airy bread.
Place dough in a greased bowl, turning once to coat the dough. Cover loosely with a clean cloth and let rise in a warm, draft-free place for 1-2 hours or until doubled.
Punch the dough down.
Roll dough into a rectangle about 1” thick. Use a sharp knife or pizza cutter to cut dough into squares.
Preheat oven to 350F°/177℃.
Spray a cookie sheet pan with oil or butter, then place rolls on an oiled pan about ½–1” apart. Cover lightly with a kitchen towel and let rise for about 30 minutes or until the dough is puffy.
Bake 12-15 minutes or until golden brown. Brush with remaining melted butter.
Remove from the baking pan and let it cool. I like to eat mine when it is still warm.