To make the dough:
Mix together 1¾ cups flour, yeast, and salt. set aside.
In a small saucepan, heat the milk, water, butter, and sugar over med-low heat until it reaches 120-130F, stirring constantly. pour into the dry mixture and beat until smooth.
Add egg and ½ cup flour and beat for another 2 minutes.
Gradually add enough flour to make a soft dough (probably cup or two).
Knead dough. cover and rest for 20 minutes.
Once dough has risen, roll out into a rectangle, approx ¼” thick. spread melted butter over top, and sprinkle filling overtop, leaving a ½” border all the way around.
To make the filling:
Combine brown sugar and cinnamon. (double amounts, if necessary, to cover the area.)
Roll the dough as for a jelly roll, keeping it as tight as possible. when you get to the end, pinch the dough along the top and cut into 12 rounds, using a knife or bench scraper. place rolls on a greased pan and bake at 375 for 15-20 minutes until golden brown. let cool slightly, then top with glaze.
To make glaze:
Combine powdered sugar, butter, vanilla, and hot water and stir until you reach a smooth consistency.