01 - Combine warm milk and active dry yeast in a small bowl. Allow to sit until foamy, about 5 to 10 minutes.
02 - Whisk all-purpose flour, unsweetened cocoa powder, and salt together in a large bowl.
03 - In the bowl of a stand mixer, combine granulated sugar, eggs, melted butter, vanilla extract, red food coloring, and yeast mixture. Mix until integrated.
04 - Gradually incorporate dry ingredients into wet mixture. Knead with dough hook for 8 to 10 minutes, or knead by hand on a lightly floured surface, until dough is smooth and elastic.
05 - Transfer dough to a greased bowl. Cover and let rest in a warm area until doubled in volume, approximately 1 to 1 1/2 hours.
06 - Deflate dough and transfer to a floured surface. Roll out to a 16 by 12-inch rectangle.
07 - Spread softened butter evenly over the dough. Distribute brown sugar and ground cinnamon across the surface.
08 - Starting from the long edge, roll dough tightly into a log. Use a sharp knife or dental floss to slice into 12 uniform pieces.
09 - Arrange rolls cut side up in a greased 9 by 13-inch baking dish. Cover and allow to rise until puffy, 30 to 45 minutes.
10 - Set oven to 350°F. Bake rolls for 22 to 25 minutes, or until lightly golden.
11 - Beat cream cheese and butter in a bowl until smooth. Gradually mix in powdered sugar and vanilla extract, continuing to beat until fluffy. Adjust consistency with milk as needed.
12 - Spread frosting generously over warm cinnamon rolls. Serve immediately.