In the bowl of a stand mixer fitted with the hook attachment add the milk, sugar, butter, salt, yeast, and food coloring. Mix that to combine everything.
Add the eggs and sour cream. Mix again to combine.
Add the flour and cocoa powder, mix well. Turn the stand mixer on medium speed and mix for 5 minutes until the dough is smooth and elastic. If the dough is too sticky, add a little more flour, a tablespoon at a time until it comes together and does not stick to the bowl.
Cover the bowl with plastic wrap and place it in a cool, draft free area for 1.5-2 hours. The dough should double in size.
Once the dough has doubled in size, empty the bowl onto a well floured counter. Lay the dough out and roll it out to 18 inches by 12 inches.
For the filling, mix the cinnamon and sugar together. Spread the butter out over the rolled out dough. Sprinkle the cinnamon and sugar mixture evenly over the rolled out dough.
Butter a 9x13 inch baking pan well with softened butter. Starting with the side closest to you, roll the dough up and away from you to create a log. Cut the log into 12 equal pieces and place them in the pan. If you are baking the cinnamon rolls immediately, let them sit at room temperature for an hour. If you are cooking them the next morning, place them in the refrigerator overnight. In the morning, take out the rolls and let them come to room temperature before you bake them.
Preheat the oven to 375 degrees. Bake the rolls for 35-40 minutes until the buns are browned and puffy. Let them cool a few minutes while you make the icing.