To make dough:
Cream butter, sugar and salt together using an electric mixer. Stir in egg. Add 2 cups flour and yeast. Pour water in all at once and mix.
Gradually add 1-3/4 cups flour to make a soft dough. Knead 5 minutes on lightly floured surface. Place dough in a greased bowl. Cover and let rise until double, about 45 to 60 minutes.
Punch down and roll out dough to a 18 x 10-inch rectangle. Brush dough with 3 tablespoons melted butter. Mix sugar and cinnamon together and sprinkle entire amount evenly over dough.
Roll up from long side; seal edges. Cut roll into 12 slices. Using three greased 8-inch square pans, place 4 rolls per pan, cut side up. Cover and let rise until double, about 45 minutes. Bake at 350ºF for 16 to 18 minutes. Cool.
Mix powdered sugar, vanilla and enough cream to make icing of pouring consistency. Drizzle frosting evenly on all rolls.