Spray a 9x13 inch baking dish with cooking spray. Set aside.
Proof the yeast by pouring the warmed milk into bowl with sugar and yeast. Whisk to mix and set aside for about 5 minutes, or until bubbles or foam form on the surface.
Whisk in the sourdough discard and the egg.
Next, add the flour, softened butter, and salt. Mix dough until it begins to come together. Continue kneading or mixing the with a mixer until the dough is soft and not too sticky. It should stick to the bowl, but pull away clean. Mix in 1 to 2 tablespoons of extra flour if needed.
Cover the bowl with plastic wrap and allow to rise until doubled (about 1 to 2 hours )in a warm, draft free location.
While waiting to rise, mix the softened butter, brown sugar, and cinnamon together into a spreadable paste and set aside.
When dough has doubled in size, transfer to a lightly floured work surface and roll dough into a large rectangle, or about 18x12 inches.
Spread the softened butter and cinnamon sugar mixture over the entire surface of the dough.
Starting at a short end a 12" side of the rectangle), roll the dough up tightly, jelly roll style. Pinch the dough together at the seam to secure.
Cut the roll into 12 equal slices by lightly marking the center and quarter lines if needed. Place the slices in the prepared baking dish. Cover with plastic wrap and set to rise in a warm, draft free location for 30-45 minutes.
Preheat oven to 350℉ degrees. Place the baking pan of risen cinnamon rolls in the prepared oven for 25 minutes, or until puffy and golden brown.
While baking make the cream cheese icing by mixing the softened butter and softened cream cheese with an electric mixer. Add the powdered sugar, vanilla extract, and milk or cream until the icing is creamy and spreadable.
After removing the cinnamon rolls from the oven, cool for 15 minutes, or until rolls are just slightly warm, before spreading the cream cheese icing over the rolls. Serve warm or cold.