Put 1/4 cup of the warm milk in a small bowl. Add the yeast and sugar and whisk or stir to dissolve. Set the bowl aside for 8 - 10 minutes, until the mixture looks foamy. If the yeast isn't foamy after 15 minutes, start over with a new package.
Put the flour and salt in the large bowl and whisk to blend. Make a well in the center of the flour mixture, and pour the yeast mixture into the well. Then pour the remaining 1 cup warm milk and the melter butter into the well. Using the wooden spoon, stir together the flour mixture and the liquids until you get big, shaggy clumps of dough that start to stick together.
Sprinkle a little flour on your work surface. You can always add more later, so don't sprinkle too much. Dump the dough clumps out of the bowl onto your work surface. Dip your hands in flour and start kneading the dough. Keep kneading until the dough is smooth and springy and no longer sticky. It will take about 10 minutes. Lightly flour your hands and the surface if the dough starts sticking. It should feel tacky, like tape, but not sticky and gooey. The bench scraper is handy for scraping up any bits of dough stick to the table, and to help you move the dough around.
Wash out the large bowl and rub the inside with a think layer of vegetable oil or coat with pan spray. Shape the dough into a ball and put it in the bowl. Lightly rub or spray the top of the dough with a little oil. Cover the bowl with plastic wrap. Set the bowl aside and let the dough rise for 45 - 60 minutes, until it is twice as big.
While the bread dough finishes rising, put the brown sugar and cinnamon in the medium bowl and whisk together until well blended. Smash any brown sugar lumps to break them up. Set aside. Crack the egg into 1 of the small bowl and beat with the fork until blended. Set aside.
Sprinkle 3 tablespoons flour on the work surface. Turn the risen dough out of the bowl onto the floured surfaced and shape into a rough rectangle. Sprinkle another tablespoon of flour on top. Sprinkle from the edge closest to you, roll gently but firmly to the edge opposite you and then back again twice. Be careful not to roll the pin off the edge of the dough, or the dough will stick to the surface. Turn the dough a quarter turn and roll up and back again twice. When you turn the dough, it should move easily. If it doesn't gently lift area of stuck dough. loosening it with the small metal spatula, and sprinkle some more flour underneath. Repeat the rolling up and back and turning the dough until you have a 15 by 12 inch rectangle.
Brush any excess flour from the top and bottom of the dough with the large brush, and clean up any extra flour from around the dough with the bench scraper. Position the rectangle so you are facing a long side.
Using the small pastry brush, brush a thin coating of egg all over the top of dough. (you won't need all of it.) Use your finger to scrape the filling onto the dough and spread it evenly over the surface, leaving a 1 inch wide border uncovered along the long side opposite you.
Starting at the long side closest to you, roll up the dough into a long, keeping it fairly tight as you go. When you reach the opposite side, roll the dough on top of the uncovered border. Roll the log backward, so the seam is on top, and pinch all along the seam to seal it.
Lightly butter the cake pan or spray with pan spray. Using the serrated knife, cut the log crosswise into 10 rolls each about 1 1/2 inches wife. Use a gentle sawing motion when you cut so that you don't flatten the log. Arrange the rolls in the prepared cake pan, evenly spacing 8 rolls around edge of the pan and putting 2 rolls in the center
Cover the pan with plastic wrap and set in a warm place. Let the rolls rise for about 1 hour, or until they are nearly twice as big fill almost all of the open spaces in the pan.
After the rolls have risen for about 30 minutes, position an over rack in the center of the oven, and preheat the oven to 350F. That way, the oven will be ready when you are ready to bake.
Bake the rolls for 30 - 35 minutes, until they are golden and the sugar is bubbling around the edges. Using the oven mitts, transfer the pan to the cooling rack. Let cool for 10 - 15 minutes.
Put 1 cup powdered sugar in the other small bowl. Add the water and whisk until well blended and completely smooth. The icing should be fairly thick, because it thins out when it hits the warm rolls. If it is thin and runny, add a little more sugar.
Using the spoon, drizzle the icing over the top of the warm rolls in any pattern you like. Eat them while they are warm!