Grease two 9 x 13-inch pans; set aside.
In large bowl, dissolve 1 teaspoon sugar in warm water. Stir in yeast; let stand for 10 minutes, or until foamy. Whisk in warm milk, sugar, egg and butter.
Add 3 cups flour and salt; mix with wooden spoon or dough whisk until smooth. Slowly stir in an additional 4 1/2 cups flour. Stir briskly until well mixed. If needed, gradually add remaining 1/2 cup flour to make soft dough.
On lightly floured surface, knead dough about 8 - 10 minutes, until smooth and elastic. Cover; let rest in warm place for 10 minutes.
Prepare filling: In small bowl, combine sugars and cinnamon; set aside
Divide dough into 4 equal balls. (see note)
Roll one dough ball into 15x10-inch rectangle. Brush with melted butter and sprinkle with 1/4 of cinnamon sugar mixture. Starting with long edge, roll up tightly like a jelly roll. Pinch seam to seal. With sharp knife, slice roll into 1 1/2 -inch pieces. Place cut sides up in prepared pan. Repeat with remaining 3 dough balls (see note).
Cover and let rise in warm place until indentation remains after lightly touching, about about 45 minutes.
Preheat oven to 375°F.
Bake 20 minutes or until rolls are lightly browned. Remove rolls from pan to a wire rack; let cool.
Prepare glaze: In small bowl, combine icing sugar and milk; stir until smooth. Adjust sugar/milk to get desired consistency. Drizzle warm rolls with glaze.