"This is my go-to recipe for cinnamon rolls, sticky buns, etc. The sourdough starter we use has been passed down for generations in my husband's family. It gives the rolls the characteristic sourdough punch that contrasts well with the sweet filling and frosting."
Mix 1 cup flour, starter, milk, white sugar, and yeast together in the bowl of a stand mixer. Let stand until spongy and bubbling, about 5 minutes. Add 1/2 cup butter, egg, and salt; stir to combine. Add remaining flour 1 cup at at time until a soft, slightly sticky dough forms.
Transfer dough to a floured work surface; knead until dough comes together, 3 to 5 minutes. Place in a greased bowl. Cover with plastic wrap; allow to rest until doubled in size, about 1 hour.
Preheat oven to 375 degrees F (190 degrees C). Grease a 9x13-inch baking pan.
Punch dough down; transfer back to the floured surface. Roll into a square 1/4-inch to 1/3-inch thick. Spread 1/2 cup butter on top; sprinkle brown sugar and cinnamon on top. Roll dough up tightly; pinch seam together.
Trim the edges and cut the log into 8 equal pieces using a sharp knife. Place rolls in the prepared baking pan. Cover with plastic wrap; let rise until not quite doubled in size, about 45 minutes.
Bake in the preheated oven until golden brown, about 35 minutes. Remove from oven; cool for 20 minutes.
Mix confectioners' sugar, cream cheese, 1/4 cup butter, and vanilla extract together until frosting is smooth and fluffy. Top each cooled roll with an equal amount of frosting.