Start by feeding your sourdough starter the night before, ensuring it is active and bubbly.
Heat a small sauce pan on the stove and add in your butter. Allow the butter to melt completely before taking it off the heat and adding in your cold milk. This will bring the butter temperature down so it will not scold and kill the sourdough starter in your dough.
Once the milk and butter mixture is warm but not hot, add it into your stand mixer along with the remaining ingredients.
When the ingredients are incorporated in the mixer, allow it to knead on low for 5-7 minutes.
Place a clean towel over the bowl and allow the dough to rise in a warm place for 3-4 hours.
After the bulk rise is done, shape the dough into 9 equal sized balls and place into a greased baking pan. Place a towel over the rolls and allow them to rise for another 2-3 hours.
Preheat the oven to 375 degrees F and bake the rolls for 25 to 30 minutes, ensuring the tops are golden brown.
Once the rolls are golden, take them out of the oven and immediately brush the top with melted butter.