In the bowl of a stand mixer, add the warm water. Sprinkle the yeast and about 1 tsp of the sugar. Let stand until foamy. Add the warm milk, warm heavy cream, the egg, the remaining sugar and salt. With the dough hook attached, run the mixer at low speed just to incorporate the ingredients.
Add 3 cups of flour, one cup at a time, and beat on low speed after each addition. The dough will start to gather into a shaggy mass. Add the remaining cup of flour and continue to beat until incorporated. Then slowly build up the speed to medium and mix the dough for about 8-12 minutes, scraping the sides and bottom of the bowl when necessary.
You will see the dough starting to gather into the center and attaching itself into the dough hook. Sprinkle a little amount of flour (about half a teaspoon at a time) into the bowl and continue mixing. This should help the dough to release from the bottom of the bowl. You can add up to two tablespoons of flour and you should soon see the dough starting to gather in the center of the bowl. As you approach the 12 minutes mark, you should hear the dough slapping the sides of the bowl as it clings to the dough hook. This is a good sign that your dough is ready for proofing.
Gather the dough into a ball, sprinkle a little bit of flour into a bowl, and place the ball of dough inside it. Cover the bowl with a kitchen towel and set it on a warm place for one hour to one hour and a half, until the size of the dough is doubled. Meanwhile, Grease two 9 inch round cake pans.
Divide the dough into 16 equal portions. I usually cut the dough in half, then cut each portion in half again, and so on until I yield 16 equal pieces. Roll each portion into a log of about 8-10 inches in size, then twist each log into a coil. Tuck the ends underneath. Place each assembled dough inside the round pans, giving about an inch of space between each roll. Each 9 inch round cake pan should have 8 rolls each. Cover the rolls loosely with plastic wrap and let rise again until double in size, about an hour or so.
Alternatively, you can make two loaves by dividing the dough into 2 portions, then divide each portion into 3 portions for a total of six. Roll each portion into a rough rectangle, then roll it into a cylinder starting on the short edge. Arrange 3 cylinders of dough in each pan. (See photos in the post)
Preheat oven to 350 F. Make the egg wash by lightly beating one egg with 1 tablespoon of milk. Brush the surface of the rolls with the egg wash without letting the fluid drip to the sides. Bake in a 350 F oven for 23-25 minutes or until rolls are deeply golden on top. A thermometer should read 200 F. Once it reaches that mark, the bread is done. For loaves, bake it for 3-5 minutes more. To make the glaze, mix three teaspoons of sugar with two teaspoons hot water, stir it until the sugar is dissolved, and brush over the bread.