Before you get started on mixing your dough, you'll make your tangzhong. Whisk milk and flour together in a small saucepan.
Cook the tangzhong over medium/low heat, stirring constantly, until it thickens into a paste that is similar to pudding (about 2–3 minutes). For precision, use your digital thermometer and heat to 148-155 F. Do not overheat, or your mixture will be too thick.
Scrape into a bowl immediately to prevent further cooking, cover, and let cool to room temperature before adding to your dough.
In a large bowl or stand mixer bowl, add the tangzhong, sourdough discard, egg, egg yolk, whole milk, white sugar, instant dry yeast, and vanilla. Whisk all the wet ingredients until smooth.
Add the flour and salt to the wet ingredients, and transfer to the stand mixer and knead on Speed 1 or knead by hand for about 3-4 minutes until the dough comes together.
Once the dough has come together, add the softened butter slowly by the Tablespoon. Once you've mixed in a Tablespoon, add another until all of the butter has been worked into the dough.
Mix the butter into the dough with the stand mixer set to Speed 1, or you can do this by kneading the butter in slowly by hand. The dough should be smooth and slightly sticky.
Spray a clean mixing bowl large enough for the dough to double in size with cooking spray, and transfer the dough to the bowl covering it with a lint-free kitchen towel or lid. Allow the dough to rest 20 minutes.
After the 20 minute rest, knead the dough by hand for a minute or two to get the dough even softer and to work the gluten. Once you've finished this kneading step, cover the bowl again.
Allow the dough to rest about 1 ½ hours at room temperature and the dough is ~75–90% risen. You don't want this dough to proof double fully at this rising point.
Make sure your butter is completely softened before mixing the cinnamon sugar filling.
Add the butter to a mixing bowl, then add the brown sugar, cinnamon, flour, and salt.
Using a spatula, combine all of the ingredients until you have a smooth spreadable paste.
Lightly grease a 9×5-inch loaf pan, and fit it with parchment paper (leave some overhang so you can pull the bread out of the pan).
On a lightly floured surface, turn your dough out and roll the dough into a 12×16-inch rectangle.
Spread the cinnamon filling evenly over the dough, leaving a ¼-inch border around the edges.
Using a pizza cutter or sharp knife, cut the dough lengthwise into four 3-inch-wide strips.
Next, cut each strip crosswise every 4 inches to create four rectangles per strip. You will have 16 rectangles, each measuring approximately 3×4 inches.
Fold each rectangle in half like a taco with the cinnamon filling tucked inside, creating a 3×2-inch folded piece.
Layer each section filling upright into the pan until all the sections are snuggly fitted into the pan.
Cover the pan loosely with plastic and let rise for 45 minutes to an hour, or until the dough is noticeably puffy and the highest layers rise just above the rim of the pan.
Preheat oven to 350°F (175°C).
Right before you bake your bread, pour the heavy cream over the top to give the loaf extra moisture.
Transfer the bread to the preheated oven, and bake for roughly 45-50 minutes. If the top is browning too quickly, tent loosely with foil during the last 10–15 minutes.
Allow the bread to cool while you whip up your cream cheese icing.
Place the cream cheese and softened butter in a bowl, and beat on high with hand mixers until smooth.
Add the vanilla, powdered sugar, and salt to the bowl, and beat into the icing.
Beat milk 1 Tablespoon at a time into the glaze, until the consistency is runny and can easily drizzle on top of the bread.
Remove the bread from the pan, and drizzle the icing over the top of the warm bread. Serve and enjoy!
