Pour warm milk (110-115 degrees F) into the bowl of a stand mixer. Add 1 teaspoon of the sugar and the active dry yeast. Stir, and let it stand for about 10 minutes until frothy. This means that the yeast is good. If not, start over with new yeast.
With the mixer on medium speed (use the whisk attachment), mix the yeast mixture, melted butter, ⅓ cup granulated sugar, 2 eggs, and salt until well-combined.
Switch to the dough hook attachment on the stand mixer. On medium speed, add 3 cups of bread flour, 1 cup at a time. Add the remaining flour in ¼ cup increments as needed, until a dough forms. Increase to medium-high speed and mix/knead for 3 to 4 minutes. If it’s sticking to the bowl too much, continue adding flour in ¼ cup increments. I ended up using 4 ¼ cups of flour. The dough should be moist, manageable, and slightly sticky.
Transfer the dough to a floured surface, and knead by hand for another 3 minutes, sprinkling more flour as needed, until the dough is manageable and springs back slowly when poked.
Form a ball with the dough, pinching the bottom, and transfer to a lightly oiled bowl (vegetable oil is fine). Make sure to coat all sides of the dough with oil. Cover the bowl with plastic wrap tightly, and let it rise for about 1.5 hours or until doubled in size in a warm and draft-free environment (see note below on "creating a warm environment").
Make the cinnamon and sugar filling: Whisk light brown sugar with ground cinnamon until evenly combined. Set aside.
Grease a 9x5 baking pan with butter. Set aside.
After the dough has doubled in size, punch it down to remove the air. Roll it out into a 9x18 inch rectangle. Brush with the egg and water mixture (1 egg beaten with 1 tablespoon water), leaving 1 inch borders. Sprinkle with the cinnamon and sugar mixture evenly. Starting from the shorter side, roll the dough as tightly as you can to form a 9-inch log. Pinch to seal the dough. Tip: when rolling the dough, try not to apply too much pressure in the middle so that it’s uniformly rolled.
Transfer the rolled dough to the greased baking pan. Cover with plastic wrap and let it rise for 1 to 1.5 hours or until puffed up in a warm and draft-free environment.
While the dough is rising, preheat the oven to 350 degrees F.
After the dough has risen, make the egg wash by whisking 1 egg with 1 tablespoon of whole milk. Gently brush the top of the puffed up dough with it. Bake for 35 minutes until golden brown. Tent with foil after about 25 minutes to prevent it from browning too much.
Once ready, remove from the oven and let it cool for 15 minutes. Then, remove from the pan and let it cool completely on a wire rack. Slice and serve. Enjoy!