In a large bowl, combine 2 cups of flour, yeast, sugar, salt, and cocoa powder. 
Heat the milk, water, and butter until warm (about 110°F). Pour the warm mixture into the flour mixture and stir. Add the egg and food coloring, mixing until combined. 
Gradually add the remaining flour, 1/4 cup at a time, until a soft dough forms. Knead the dough on a floured surface for about 5-7 minutes until smooth and elastic. 
Place the dough in a greased bowl, cover, and let rise in a warm place for about 1 hour, or until doubled in size. 
While the dough rises, prepare the filling by mixing the softened butter, brown sugar, and cinnamon together in a small bowl. 
Once the dough has risen, roll it out on a floured surface into a rectangle, about 15×9 inches. 
Spread the cinnamon-sugar filling evenly over the dough. 
Roll the dough tightly from the long side into a log, then cut into 9 equal rolls. 
Place the rolls in a greased 9×13-inch baking dish. Cover and let them rise for another 30 minutes. 
Preheat your oven to 350°F (175°C). Bake the rolls for 20-25 minutes, or until lightly browned. 
While the rolls are baking, prepare the glaze by beating the cream cheese, butter, powdered sugar, vanilla, and milk until smooth. 
Once the rolls are baked and slightly cooled, spread the cream cheese glaze over the warm rolls. 

Prep Time: 20 minutes
Rising Time: 1 hour 30 minutes
Cooking Time: 25 minutes
Total Time: 2 hours 15 minutes
Kcal: 320 per roll
Servings: 9

Enjoy your deliciously festive Red Velvet Cinnamon Rolls!