Add the active sourdough starter, dark brown sugar, and warm milk to the stand mixer bowl with the paddle attachment. Mix on low speed until well combined.

Add melted unsalted butter, salt, and the room temperature egg to the mixture. Continue mixing on low until fully incorporated.

Switch to the dough hook attachment. Add the bread flour in increments of 70g while mixing on medium speed. Scrape the sides of the bowl between additions. Knead for an additional 5 minutes until the dough feels tacky and pulls away from the bowl.

Cover the bowl with a towel or plastic wrap and let the dough rise in a warm spot until doubled, about 6-7 hours at 70°F.

Turn the risen dough onto a floured surface and roll it out into a 16x12 inch rectangle.

Spread softened butter evenly over the dough surface.

Combine dark brown sugar and ground cinnamon in a small bowl, then sprinkle it evenly over the buttered dough.

Roll the dough starting from the long edge closest to you into a log. Trim uneven edges. Cut into 9 equal pieces.

Grease a 9x9 inch baking dish or large cast iron skillet with butter. Place rolls in the dish spaced 1/2 to 1 inch apart.

Cover with a damp towel and allow rolls to rise until puffy and noticeably grown, approximately 3-4 hours at 70°F. Alternatively, refrigerate overnight and then allow to rise at room temperature before baking.

Preheat oven to 350°F. Warm the heavy cream to just before baking.

Pour warm heavy cream over the rolls.

Bake rolls at 350°F for 30-35 minutes, or until tops are golden brown and internal temperature reaches 190°F.

Remove from oven and transfer to a wire rack to cool slightly.

While rolls cool, beat unsalted butter and cream cheese together until smooth. Add powdered sugar and heavy cream and mix until creamy.

Spread cream cheese frosting over warm cinnamon rolls.