• In a bowl of a stand mixer fitted with a dough hook, add the milk and stir in the yeast and one tablespoon of sugar. If using active dried yeast, leave it to sit for 5-10 minutes until foamy.
• Add to it the remaining sugar, eggs, flour, and salt. Turn the mixer on low and combine until it forms a thick but slightly sticky dough. Mix this dough for around 5 minutes to begin developing the gluten.
• Add in the cubed butter, a few pieces at a time. Incorporate each cube before the next addition.
• Turn the mixer on medium and keep it mixing until the sticky dough starts to strengthen and come together and pull away cleanly from the sides of the bowl. Mix the dough for the best gluten development and brioche crumb for at least 15 minutes. Proper gluten development will allow you to stretch the dough so thin you can almost see through it. This is called the 'window pane' test.
• Pull the dough from the bowl onto a bench and form it into a ball. Place the dough ball into a clean bowl and cover it. Let it proof at room temperature for 1- 2 hours until doubled in size. The rising time will depend on room temperature.
• Deflate the dough gently and reshape it into a ball again. Cover it with an airtight lid or plastic wrap and place it in the fridge overnight. This step can be shortened, but 8-12 hours long cold proof gives the best flavor.

Shaping

• Pull the cold dough from the bowl and tip it onto a floured bench. Roll the dough out into a 12x18-inch (30x45-cm) rectangle.
• Spread softened butter over the dough. In a bowl, mix together the brown sugar and ground cinnamon. Sprinkle the cinnamon sugar over the butter.
• Tightly roll the dough to form an 18-inch/45cm long log. Slice the log into 12 even-sized pieces. The unraveling end parts of each roll can be tucked under to keep them tight.
• Line a 9x13 inch/23x33cm baking dish. Place the rolls in and cover them with a lightweight, slightly dampened kitchen towel or plastic wrap (to stop the tops drying out). Let them rise at room temperature, puffy, and double in size.
• Preheat the oven to 350°F/180°C.
• Bake the brioche cinnamon rolls for approximately 28-30 minutes until puffed up and browned on the tops. If the tops are browning too fast, cover them with aluminum foil halfway through baking.
• After baking, let them cool for 10 minutes before frosting.

The frosting

• Beat the cream cheese in a mixer until smooth and creamy. Add the confectioners’ sugar, vanilla, and milk. Beat it together until creamy.
• Spread the icing over the still-warm cinnamon rolls and serve.