Heat the milk and 3 Tbsp. of the butter until warm (about 110ºF).
Sprinkle in the yeast and let rest 10 minutes.
Add the yeast to the bowl of a stand mixer (fitted with a dough hook), along with 1 Tbsp. granulated sugar, salt, and 1 cup flour.
With the mixer on low, gradually add the remaining flour, then the sourdough starter. Increase the mixer speed to medium and let knead 5 minutes until the dough comes together. Keep an eye on the moisture of the dough. Once kneaded, the dough should form a solid ball and be sturdy but soft when you poke it. If the dough is wet or sticky, add a Tbsp. of flour.
Place dough in a lightly-oiled bowl, cover with a clean dish towel, and let rise in a warm spot for 1 hour until doubled in size.
Dump dough onto a floured surface, then roll into a large rectangle. Melt remaining butter and brush most of it over the dough (save a small amount of melted butter to brush over rolls right before baking), then sprinkle with cinnamon and 1/4 cup granulated sugar.
Roll tightly, making sure to pinch the seam tightly. Cut rolls to desired size, then place either in a baking pan or into individual muffin tins.
Cover with a clean dish towel and place in a warm place to rise. Let rise 30-45 minutes, until the rolls are big and puffy, but not quite doubled in size.
When the rolls are almost done rising, preheat the oven to 350ºF.
Brush rolls with remaining melted butter, then bake 25-30 minutes until golden brown.
To make the cream cheese frosting, combine all frosting ingredients in a bowl and mix until smooth. Drizzle over warm cinnamon rolls.