Mix flour, sugar, yeast, salt, and cocoa powder.
Combine warm milk, melted butter, egg, and food coloring.
Add wet ingredients to dry ingredients gradually.
Knead dough until smooth and elastic.
Place dough in greased bowl for rising.
Let rise for 1 hour until doubled.
Roll dough into 12x18 inch rectangle.
Spread softened butter over entire dough surface.
Sprinkle brown sugar and cinnamon mixture evenly.
Roll dough tightly from long side.
Cut into 12 equal pieces using sharp knife.
Place rolls in greased baking dish.
Let rise again for 30 minutes.
Bake at 375°F for 20-25 minutes.
Beat cream cheese frosting ingredients until smooth.
Frost warm rolls before serving immediately.