Beat Egg. Set aside.
Combine water, oil, sugar, and yeast in a large bowl. Allow to sit for about 10 minutes until mixture is bubbly.
Stir in salt, beaten egg and softened butter.
Add flour, mixing in about 1/2 cup at a time until dough that is no longer sticky.
Knead by hand for about 7-9 minutes.
Preheat oven to 400.
Cut dough into 18 even pieces.
Form into balls and arrange in a 9x13" baking disk.
Cover with a kitchen towel.
Sit in a warm place for 30-45 minutes, until rolls are about doubled in size.
Brush tops of rolls with milk.
Bake for 10 minutes on the middle rack until browned.