For the rolls: Mix sugar, oil, salt and water in a large bowl and add beaten egg. In 2 cups of flour, add the instant yeast and mix well. Add this to the water mixture and continue adding flour one cup at a time. I use a stand mixer with a bread hook attachment for this step. You can also use a spoon and hands. Keep working in flour until the easy to handle. Don’t work in too much flour, just enough to get the dough into a large workable mound.
Grease your mixing bowl and let the dough rise until doubled. It’s good to punch it down and let it rise again. This gives the rolls a nice texture. To make the rolls, divide the dough into two parts. Roll out in oblong pieces approximately 8”x 14.” Spread about 2-3 T of softened butter on the dough. Then sprinkle with brown sugar and cinnamon. Roll them up and cut into 1 1/2 “ widths. Place them in a 9×13 inch baking sheet. Bake at 350 until lightly browned (about 30 minutes in my oven). Do not over bake. Frost when slightly cooled.
For frosting: Melt butter on medium heat in large saucepan, stir until it starts to bubble, then add water. Stir until all the sugar is dissolved and it begins to boil. Remove from heat and cool well before adding powdered sugar and vanilla. Add the powdered sugar until it’s just the right consistency for spreading. This tends to be a runnier icing so be careful not to add too much! Enjoy!