Heat the milk in a small saucepan until it bubbles, then remove from heat. Mix in butter; stir until melted. Let cool until lukewarm.

In a large mixing bowl, combine 2 ¼ cup flour, yeast, sugar and salt; mix well. Add water, egg and the milk mixture; beat well.

Cover the dough with a damp cloth and let rest for 10 minutes.

Meanwhile, in a small bowl, mix together brown sugar, cinnamon, softened butter. It should be the consistency of frosting.

Roll out dough into a 12x9 inch rectangle.

Spread dough with butter/sugar mixture. Roll up dough and pinch seam to seal. Cut into 12 equal size rolls and place in lightly greased baking sheet.

Cover and let rise until doubled, about 30 minutes.

Preheat oven to 375 degrees F.

Bake in the preheated oven for 20 minutes, or until browned.

In 2-quart saucepan, melt butter over medium heat. Stir in brown sugar. Heat to boiling, stirring constantly. Reduce heat to low; boil and stir 2 minutes. Stir in milk. Heat to boiling. Remove from heat. Cool to lukewarm, about 30 minutes.

Gradually stir powdered sugar (½ cup at a time)  into brown sugar mixture. Place saucepan of frosting in bowl of cold water. Beat with spoon until smooth and spreadable. If frosting becomes too stiff, stir in additional milk, 1 teaspoon at a time. Spread over rolls.