In a large bowl, add 2 1/4 cups flour, the sugar, salt, and yeast package and stir (I like to use a whisk). Set aside the last 1/2 cup of flour.
In a microwave safe bowl, add the water, milk, and butter and microwave until the butter is melted and the mixture is hot to the touch. Stir it to combine everything together.
Add the butter mixture to the flour mixture and stir.
Add the egg and just enough of the reserved flour to make a soft dough. I didn't need the full 1/2 cup. The dough is ready when it is soft, not sticky, and has an elastic consistency.
Use the remaining flour (from the 1/2 cup - or add more, if you used the full 1/2 cup) to flour a clean surface (I use a large cutting board). Knead the dough for 3-4 minutes. It should still be soft, not sticky. Form the dough into a ball and add to a large bowl you've lightly sprayed with non-stick spray. Cover the bowl tightly with plastic wrap and let it rest & rise for 30 minutes.
To make the filling
In a medium bowl (I just used a cereal bowl), add the cinnamon and sugar and stir to combine.
After the dough has rested for 30 minutes, roll it out into a 15" x 12" rectangle. I used a silicone baking mat, which is that exact size.
Spread the softened butter on top then sprinkle the cinnamon/sugar mixture evenly all over the dough.
Spray a 9" round pan (I used a glass pie plate) with non-stick spray and set aside.
Use a pizza cutter (or a very sharp knife) and cut the dough into six (6) 2" wide strips.
Loosely roll up one of the strips and put it in the center of your round plan. Take the next strip of dough and join it with the end of the center roll. Pinch the ends together and continue your coil - wrapping the dough loosely. Repeat with each strip of dough.
Sprinkle any cinnamon/sugar mixture that fell out while you were coiling onto the top of the roll.
Cover the pan, loosely, and allow the dough to rise in a warm place for at least 60-90 minutes. It should pretty much double in size. I made mine at night, left it on the counter overnight, and baked it in the morning.
Sally says it can rise for up to 12 hours. After rising, a couple areas had risen more than others so I pushed them down gently with the back of a wooden spoon.
Once ready to bake, preheat the oven to 350 degrees then bake for 30-35 minutes until lightly browned. After 15 minutes of baking, I covered the cake with foil so it wouldn't brown too fast.
To make the glaze
In a medium bowl (again, I used a cereal bowl), add the sifted powdered sugar, milk, and vanilla and mix with a whisk until smooth. Mine was a little thick so I added another splash of milk.
Once the cake is done, let it cool for about 10 minutes then drizzle with the glaze.