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. Measure 1/4 cup of sugar/cinnamon mixture and set aside.
Roll dough into a 7 x 24-inch long, narrow rectangle using a rolling pin. Spread 2 tablespoons very soft butter over dough, stopping at least 1/2-inch from the edges on the long sides. Sprinkle evenly with 1/4 cup of the reserved cinnamon sugar mixture. Beginning at long end of the rectangle, roll up tightly. Pinch seams to seal. Cut into 24 equal slices. Dip each roll in melted butter and remaining cinnamon sugar mixture. Place in greased 9 x 5-inch loaf pan.
Cover with towel; let rise in warm place until doubled in size, about 45 to 60 minutes.
Bake in preheated 350°F oven for 25 to 35 minutes or until bread is golden brown. Cool on wire rack for 10 minutes and then place on serving tray.
Combine all Vanilla Icing ingredients in a medium bowl and beat until creamy. Drizzle icing over warm loaf.