Dissolve yeast in warm water and let stand 5 to 10 minutes. In a large mixing bowl, beat butter, sugar and salt with an electric mixer until fluffy. Add 1 cup of the flour and the milk. Separate 1 egg. Add the yolk and remaining whole eggs to beaten mixture (refrigerate egg white to use later). Add softened yeast and beat well. Stir in remaining flour until smooth. Place in a greased bowl and cover. Let rise in a warm place until double, about 2 hours. Chill dough 6 hours.
To shape, pull each piece into a ball, tucking the edges under to make smooth tops. Place in prepared muffin cups, smooth sides up. Divide reserved dough portion into 24 pieces; shape into balls. With a floured finger, make an indentation in each large ball. Press a small ball into each indentation. Combine reserved egg white and 1 tablespoon water; brush over rolls. Cover; let rise in a warm place until double (45-55 minutes).