In a large bowl, stir together melted butter, mashed potatoes, eggs, and sugar.
Add in yeast, stir to combine.
Add in water and salt and stir to combine.
Add in flour 1 cup at a time until dough is thick. This usually takes about 4 cups of flour.
Turn dough out onto floured surface. The dough will be sticky. Knead dough until the dough is smooth and elastic and is tacky but not sticky. At this stage I often incorporate up to 1 more cup of flour into the dough. This usually takes about 4-5 minutes of kneading by hand.
If using a stand mixer, switch to the dough hook and knead dough until smooth and elastic. If dough is sticking to the sides of the bowl, add in a flour 1/2 cup at a time until it's tacky but not sticky.
Cover dough with clean dish towel and allow it to rise until doubled (about an hour).
Once the first proof is over, turn dough out onto a lightly floured surface. Knead for a few minutes and then roll dough out into a rectangle.
Melt some 1/4 cup butter. Brush melted butter onto the dough.
Sprinkle the buttered dough generously with the cinnamon/sugar mixture. I use a mixture that is a little heavier on the sugar than cinnamon.
Roll the dough up and slice into rolls of desired thickness. Honestly, these rolls are best a bit on the thin side. I have tried making them fat, but the ratio of dough to filling was not as tasty.
Place the rolls on a 9×13" cake pan or 2 9×9" cake pans. Above I used a square cake pan, which makes the rolls nice an soft. My mother always used a cookie sheet, which is very good, but makes for crustier outsides.
Allow rolls to rise for about an hour.
Pre-heat the oven to 350 degrees Fahrenheit. Bake the rolls for 25 minutes or so.
Ice as desired. My mother’s icing was just a simple combination of powdered sugar, milk, and a teaspoon of vanilla. Use as much milk as you would like to make the icing as thin as you like.
Notes
Can use 2/3 cup potato flakes instead of 1 cup mashed potatoes.