In a big mixing bowl, whisk together your 2 cups of flour, sugar yeast, and salt.
In a heat safe bowl, combine the water and butter to get it heated up slightly. (cut butter into tablespoons). Heat in the microwave for 30-45 seconds warm to touch, but not hot. The butter will not be melted completely.
Pour that into your dry ingredients, and add in your 1 egg.
Add in 2 more cups of flour and mix again. It should start looking shaggy at this point, (your dough). It will also be difficult to stir. Once it reaches that point, set the spoon to the side and use your hands to mix and knead the dough.
Your dough will be sticky, so add another 1/4 cup flour and continue to mix and knead by hand. It should turn into a huge smooth mass, that is soft and tacky.
WIth a clean finger, press it into the dough. If your finger comes out sticky and full of dough. add another 1/4 cup of flour to get it to the right consistency. When it is ready roll into a nice ball and let it rest uncovered for 15 minutes.
When the 15 minutes are up, the dough should have puffed up quite a bit, but not quite doubled in size.
Place the dough on a lightly floured surface and pat it into a nice rectangle that will be imperfectly shaped. Roll it in a 10x15 inch rectangle using your rolling pin.
Spread the room temp butter into a thin even layer, leaving about 1/2 inch border all around the outside of the dough.
Working from the 15 inch end of the dough, roll it up into a log. Place your nads at each end of the log and give it a gentle squeeze into a strong log roll of dough. It may have stretched out a but during the rolling process so this brings it back together.
To achieve the best results while cutting these cinnamon rolls use unflavored dental floss to cut the rolls. If you don't have any dental floss you could also use sewing thread. If neither one of those please use a very, very sharp knife and saw the rolls back and forth. Don't press straight down this will squish your cinnamon rolls too much.
When using the floss slide it underneath one end of the cinnamon roll and toss both ends of the floss over the top. Pull them through to cut them, or create a cut. Cut off the two ends of the log, and then cut the remainder in 12-15 rolls.
Cut the entire log in half, and then cut those two halves in half to create 4 segments. This honestly is up to you this part of the recipe.
Place the rolls in a 10x15 greased pan with butter, or even 9x13 (you could also use two 9" round pans by placing your rolls in each). It's OK if all the rolls are touching. See NOTES for OVERNIGHT INSTRUCTIONS.
Preheat the oven to 350 (first remove the rolls if you proofed them inside) and check on the rolls . They should have gotten bigger at this point.
Bake for 25-30 minutes or until the tops are a light golden brown. While they cool, make the icing.