In a large bowl, combine the active sourdough starter and milk.
Add melted butter and sugar; mix until smooth.
Beat in the egg until fully incorporated.
Gradually add the flour and salt, mixing until a dough forms.
Knead the dough for about 10 minutes until smooth.
Place in a greased bowl, cover, and let rise for 1-2 hours until doubled.
Roll out the dough into a rectangle (about 1/4 inch thick).
Spread softened butter over the dough, then sprinkle with cinnamon and brown sugar.
Roll tightly from the long end and cut into 12 equal pieces.
Place rolls in a greased baking dish, cover, and let rise for another 30-45 minutes.
Preheat the oven to 350°F (175°C) and bake for 25-30 minutes until golden.
For icing, mix powdered sugar, cream cheese, and milk until smooth; drizzle over warm rolls.