In a large bowl, mix the sourdough starter, milk, and melted butter.
Add the sugar and the egg, whisking until combined.
Gradually incorporate the flour and salt, mixing until a dough forms.
Knead the dough on a floured surface for about 10 minutes.
Place the kneaded dough in a greased bowl, cover, and let it rise for 1-2 hours until doubled in size.
Roll the dough out into a rectangle, about 1/4 inch thick.
Spread melted butter over the rolled dough.
Mix cinnamon and brown sugar together; sprinkle evenly over the buttered dough.
Roll the dough tightly from the long side and slice into 12 equal pieces.
Place the rolls in a greased baking dish and let rise for another 30 minutes.
Preheat the oven to 350°F (175°C) and bake for 25-30 minutes until golden brown.
Mix powdered sugar and cream cheese with a splash of milk to make icing; drizzle over warm rolls.