Begin with an active, bubbly starter. It should be recently fed and at or near its peak.
Add your sourdough starter, bread flour, all-purpose flour, sugar, eggs, salt, milk, and butter to the bowl of a stand mixer with a dough hook attachment. Knead until smooth and glossy. It's a very wet dough and may take 10-15 minutes or longer to come together in the stand mixer. Don’t add more flour.
Cover the dough with plastic wrap, a damp towel, or a tight-fitting lid and place in a warm place for 6 to 8 hours or until doubled.
In a separate bowl, combine softened butter, brown sugar, and cinnamon. Stir until smooth.
Lightly dust a work surface with flour, then roll out the dough into a large rectangle that is roughly 1/4 inch thick. Spread the filling evenly over the top of the dough.
Roll the dough up tightly, beginning at one of the long sides. When you get to the end, pinch the edge to create a seam.
Slice to make 12 even rolls. A bench scraper or unflavored dental floss is handy. Place the rolls into a well-seasoned 14" cast iron skillet or baking dish.
Cover and allow to rise until doubled, around 2-6 hours or overnight in the fridge. Enriched doughs tend to take longer to rise.
Preheat oven to 375 degrees. Bake for 30-35 minutes or until the rolls are lightly browned and the dough is cooked through. Allow them to cool a bit before frosting.
In a medium saucepan over medium heat, add cream cheese, heavy cream, maple syrup or honey, and vanilla extract. Stir to combine.
Use an immersion blender for an extra smooth consistency, if desired. Drizzle the frosting over the warm cinnamon rolls and enjoy!
Notes
This dough is wet. Don’t add more flour. Let the kneading continue, and the dough will become manageable. Too much flour can give brioche a tougher texture.
If you don’t have bread flour, you can use all-purpose. It will not be quite as soft as using the mix of the two flours, but it will still be yummy. Bread flour also helps the dough rise more.
The rise time will fluctuate with the temperature. The warmer the spot, the quicker the rise.
Enriched doughs tend to take a lot longer to rise compared to regular doughs.