Add the warm milk, sugar, egg, and softened butter to a large mixing bowl and stir until smooth.

Stir in the active sourdough starter until combined.

Add the flour and salt and mix until a rough dough forms.

Knead the dough by hand or with a mixer until smooth and stretchy, about 8 to 10 minutes.

Cover the bowl and let the dough rest at room temperature for 8 to 12 hours, or until doubled.

Lightly flour your counter and turn out the risen dough.

Roll the dough into a 12×18-inch rectangle.

Spread the softened butter for the filling evenly across the surface.

Sprinkle the brown sugar over the butter in a thick, even layer.

Sprinkle the cinnamon over the sugar.

Roll the dough tightly from the long side into a log.

Cut the log into 12 equal pieces using a sharp knife or thread.

Place the rolls into a greased 9×13-inch baking dish.

Cover the dish and let the rolls rise for 1 to 2 hours, or until puffy.

Preheat the oven to 375°F.

Bake the rolls for 22 to 25 minutes, or until lightly golden on top.

Let the rolls cool slightly while preparing the icing.

Add the cream cheese and butter to a bowl and blend until smooth.

Add the powdered sugar and vanilla and mix again.

Add the milk a little at a time until the icing reaches a pourable consistency.

Spread the icing over the warm rolls and serve.