Combine 1 cup flour, sugar, dry yeast and salt in a large mixer bowl and stir until blended. Place water and butter in a microwave-safe bowl. Microwave on HIGH in 15 second increments until very warm but not hot to the touch (120° to 130°F. Butter won’t melt completely). Add to flour mixture with egg.
Beat 2 minutes at medium speed of electric mixer, scraping bowl occasionally. Add 1 cup flour; beat 2 minutes at high speed, scraping bowl occasionally. Stir in just enough remaining flour so that the dough will form into a ball.
Knead on lightly floured surface until smooth and elastic and dough springs back when lightly pressed with 2 fingers, about 6 to 8 minutes. Cover with a towel; let rest for 10 minutes.
For filling, combine sugar and cinnamon in a small bowl. Set aside.
Roll dough into a 7 x 24-inch long, narrow rectangle using a rolling pin. Spread 2 tablespoons butter over dough, stopping at least 1/2-inch from the edges on the long sides. Sprinkle evenly with cinnamon sugar mixture. Beginning at long end of the rectangle, roll up tightly. Pinch seams to seal. Cut into 24 equal pieces. TIP: Use unflavored ental floss instead of a knife to cut rolls. To, cut a piece of floss about 12-inches long. Slide floss under the roll; bring the ends up and cross over to cut each slice. Place about 2 inches apart, cut sides down, on greased baking sheets. Cover with towel; let rise in warm place until doubled in size, about 45 to 60 minutes.
Bake in preheated 350°F oven for 15 to 18 minutes or until rolls are golden brown. Cool on wire rack for at least 10 minutes.
Combine all frosting ingredients (start with 2 tablespoons milk and add more if needed) in a bowl and beat until creamy. Spread or drizzle over rolls.