Combine warm milk, active sourdough starter, and dark brown sugar in a stand mixer. Mix on low speed, then add melted butter, egg, and salt. Gradually mix in bread flour until the dough pulls away from the bowl. Knead for about 5 minutes until smooth.

Cover the dough with a towel or plastic wrap and let rise in a warm area until doubled in size, about 3 to 7 hours.

Roll out the dough into a rectangle approximately 18x12 inches. Spread softened butter, sprinkle brown sugar and cinnamon, then roll tightly and cut into 12 pieces. Place rolls in a greased baking dish.

Cover the baking dish and let rolls rise until puffy, about 2 to 4 hours.

Preheat the oven to 350°F. Pour heavy cream over rolls before baking. Bake for 30-35 minutes until golden brown.

Mix cream cheese and butter until creamy. Gradually add powdered sugar and heavy cream. Once rolls are cooled slightly, spread the frosting generously.