In a large mixing bowl, combine brown sugar, salt, hot water, and butter. Stir to mix, break up butter chunks and dissolve brown sugar a bit (there will still be a few butter chunks, which is okay).
Add cold water, then sprinkle yeast on top and let sit for 10 minutes. It will not bubble much.
Add flour 1 cup at a time and stir together with a wooden spoon until a soft dough forms. Knead the dough for a few minutes to make sure all the flour is well incorporated. (NOTE: This is a very wet and sticky dough that will stick to your hands. Dipping your hands in flour before kneading may help, but it will still stick). Cover with a tea towel and let rise in a warm place for 1½ hours.
While the bread is rising, grease two 5-x-9-inch loaf pans with cooking spray.
To make the cinnamon-sugar mixture, mix sugar, cinnamon, and flour together. Set aside.
Make the egg wash by whisking the egg and water together in a small bowl. Set aside.
Once the dough has risen, punch it down and place it onto a lightly floured surface. Form a ball and divide it into 2 equal pieces.
Working with one piece at a time on a well-floured surface, roll the dough out into a rectangle to about 7 x 22 inches and about ½ inch thick. Brush with half of the egg wash to help the cinnamon-sugar mixture stick better. Spread ⅔ cup cinnamon-sugar mix evenly over the dough, then lightly spray with water.
Roll the dough up tightly, lightly pulling as well as tucking in the sides as you roll. Pinch ends closed and drop into the prepared loaf pan seam side down. Repeat with the second piece of dough and the remaining egg wash and cinnamon-sugar mix. Cover and let rise in a warm place for 20 minutes.
Meanwhile, preheat the oven to 350°F.
Bake for 40–45 minutes. As soon as the bread comes out of the oven, brush the tops with butter. Let cool completely before slicing.