Combine dry ingredients on a bowl. (Flour, sugar, yeast, and salt).
Stir in milk, oil and egg.
Mix (electric mixer or by hand) until dough forms a soft ball.
Turn dough out onto floured surface and knead adding small amounts of flour until dough becomes smooth and still sticky but not sticking to hands.
Cover and let rest for 10 minutes in ball shape.
During rest time warm and grease 8-inch cast iron skillet.
Also, in a small bowl combine brown sugar and cinnamon.
On floured surface roll dough into 12x9 inch shape.
Spread butter and next brown sugar/cinnamon mixture evenly on dough top.
Roll up dough starting with 9-inch end and then cut off about 1⁄2 inch on each end and discard.
Using a serrated knife or dental floss cut roll into 8 even slices.
Arrange in the greased warm skillet leaving and even space between each roll for room to rise.
Cover with towel or plastic wrap and let rise to doubled in size approximately 1-1 1⁄2 hours.
Bake in brick oven at 350° for about 15 min.
Let cool in pan for 10 min.
Make frosting by combining powdered sugar, vanilla and slowly adding milk until smooth spreading consistency.
Drizzle over buns evenly.
Cool and enjoy!