In a stand mixer bowl, combine the sourdough starter, egg, brown sugar, salt, warm milk, and melted butter. Mix on low speed until blended smoothly, about 2-3 minutes.

Add the all-purpose flour and switch to a dough hook. Knead on low speed for 5-6 minutes until the dough is smooth and elastic.

Cover the dough and let it rise in a warm location for about 6-8 hours until doubled in size.

Roll the dough out into a 16x12 inch rectangle, about ½ inch thick.

Spread melted butter over the dough, leaving about 1 inch at one edge. Mix brown sugar and cinnamon, then sprinkle over the buttered dough.

Starting from the edge closest to you, roll the dough into a tight log and cut into 9 equal pieces.

Grease a baking dish and place the rolls inside, cover, and let rise for 1-2 hours until puffy.

Preheat your oven to 350°F (175°C) and bake the rolls for 30-35 minutes until golden brown.

While the rolls are baking, beat together cream cheese, powdered sugar, and vanilla extract to make the frosting.

Let the rolls cool slightly, then frost with the cream cheese frosting and serve warm.