Grease a 9-inch loaf pan and set aside.
Dissolve the yeast in warm water (105-110°F) and let sit for 5 minutes.
Combine dissolved yeast, warm milk, sugar, 1 tablespoon softened salted butter, 3 cups of flour, and salt. If you have a dough hook with a stand mixer, you may use this to stir the dough. If not, I recommend using a large bowl and a heavy wooden spoon. Gradually add in the remaining cup of flour.
When the dough starts to form a ball, remove it to a lightly floured surface. Knead the dough for 5 to 10 minutes, until it is smooth and elastic.
Then form the dough into a large ball and place it into a greased bowl. Turn it over so that all of the dough is coated with oil. Cover the loaf with plastic wrap, or a damp towel. Place the bowl in a warm spot, not too hot, no drafts. Allow it to rise for about an hour, or until doubled in size.
Preheat the oven to 350°F.
Whisk together the egg and water in a small bowl to create the egg wash. Set aside.
In a small bowl, stir together the brown sugar, cinnamon, and flour. Set aside.
Turn the dough out onto a lightly floured surface and roll the dough into a 16x8-inch rectangle.
Brush a thin layer of egg wash over the dough and sprinkle on the cinnamon-sugar mixture.
Start rolling up from one of the short sides (one of the 8-inch sides). Roll fairly tightly. Place the loaf into the prepared loaf pan. Slash the top of the loaf three times, about ¼ inch deep. Brush the loaf with 1 tablespoon melted butter.
Bake for 40 minutes on the lowest rack of the oven, check for doneness. It should sound hollow when you knock on it. If needed, then bake for another 5 minutes.
Remove the loaf from the oven. Allow it to cool in the pan for 10 minutes. Then remove the loaf from the pan and allow it to cool completely before slicing.