Start by adding water and 1/3 cup bread flour in a saucepan on the stove on medium heat. Whisk the mixture until smooth. Slwoly add in the 1/2 cup milk and whisk until smooth.
Once the mixture is thick like a slurry, remove from heat. Cover with a soft towel or plastic wrap, so it doesn't form a skin.
Now you will grab a bowl and add in 1 teaspoon of the 1/4 cup sugar, add in the warm milk, and stir to combine. Stir in the yeast, and gently stir. Let it sit 5-10 minutes or until it is frothy.
Once mixture is frothy, add in the rest of the sugar, 1/4 cup warm milk, the starter dough you made, rest of the flour, egg and salt.
Mix until it is well combined, and then knead the cinnamon roll dough for 5 minutes on low speed on your stand mixer.
Divide the 4 tablespoons of butter into 4 parts, and mix into the dough one part at a time. You will want to knead the dough for another 5-6 minutes. Scrape the bowl on occasion. YOu want the dough to form a ball.
Transfer dough to a greased bowl, cover and let it rise for an hour or until dough has doubled.
Once dough has doubled, place on lightly floured surface. Roll the dough 8x20 inch rectangle. Mix up the brown sugar, cinnamon, and melted butter.
Spread the mixture evenly all over the dough, and then sprinkle chocolate chips on top.
Roll the cinnamon roll tightly, pulling back the dough to keep it tight. Once rolled, cut dough into 10-12 rolls.
Place into a greased 9x13 pan, cover with a towel or plastic wrap and let the dough rise for an hour to hour and a half to double in size. Preheat the oven to 350 degrees.
Brush the dough with the 1/4 cup milk reserved, You won't use it all, just a bit. This will help rolls brown.
Bake in the center rack for 20-30 minutes or until the rolls are fully cooked.
Remove rolls and let them cool a bit. Then whip up the cream cheese chocolate icing, and drizzle over the top of the cinnamon rolls.
Slice and serve up these chocolate cinnamon rolls for breakfast, dessert, or snack.