In the bowl of a stand mixer, add the yeast and sugar. Set aside. In a medium saucepan add the butter and milk then warm on low until the butter melts and the mixture reaches 95 degrees F. Add the warm mixture to the yeast/sugar and stir with a wooden spoon to combine. Let sit for approximately 10 minutes to allow the yeast to dissolve and get foamy (skip this step if using instant yeast). Fit the stand mixer with the dough hook and turn to low speed. Add the eggs one at a time and then the salt. With the mixer running on low add the sourdough discard and then the flour. Increase to medium speed and beat the dough until it is soft, smooth and supple, approximately 5 minutes.
Cover the bowl and allow to proof in a warm spot for 1-2 hours or until doubled in size (proofing at 82 degrees F took approximately 1 hour and 45 minutes).
Grease the bottom of a 9x13 inch baking dish and line it with parchment paper. Lightly flour a work surface and turn the dough out onto it. Roll the dough out evenly into a rectangle approximately 10x16 inches.
In a small bowl combine the cinnamon and sugar for the filling. Spread the butter all over the dough leaving the top 1 inch uncovered. Sprinkle the cinnamon/sugar mixture evenly over top of the butter. Roll up the dough tightly to form a 16 inch log. Pinch the uncovered dough at the top to the log to seal it closed. Cut into 8 large buns and place them in the greased baking dish. Cover the rolls tightly with aluminum foil and allow to rise for about 2 hours or until doubled OR place in the fridge overnight for up to 12 hours.
If the buns were in the fridge overnight, remove them and allow to proof in a warm spot for 1-2 hours until they are puffy (at 82 degrees F this took about 1 hour).
Preheat the oven to 375 degrees F, remove the aluminum foil from the buns and bake for 25 minutes or until golden brown on top. If the buns are browning too quickly cover them loosely with the aluminum foil about halfway through the bake time. Remove from the oven and allow the buns to cool in the pan on a wire rack while you make the frosting.
In the bowl of a stand mixer fitted with the paddle attachment or in a medium bowl with a hand held mixer beat the cream cheese and butter together on high until smooth. Add the icing sugar and vanilla extract then beat again on low to combine. Once combined, beat on high for 2 minutes. Spread the frosting over the warm rolls before removing them from the pan or remove the rolls first and let everyone serve themselves frosting.