In a mixing bowl, combine warm milk, granulated sugar, and active dry yeast; let it sit until foamy (about 5-10 minutes).

Mix in melted butter, egg, cocoa powder, red food coloring, and half the flour until smooth.

Gradually add the remaining flour, kneading until a soft dough forms (approximately 5-7 minutes).

Transfer the dough to a greased bowl, cover it with a kitchen towel, and place it in a warm spot to rise until doubled in size, which should take about 1 hour.

Roll the dough on a floured surface into a rectangle. Spread melted butter over the surface, then sprinkle evenly with cinnamon and brown sugar. Roll tightly from one end and cut into equal pieces.

Place the sliced rolls in a greased baking dish, ensuring they are snug but not tightly packed. Cover and let rise again for 30-45 minutes, or until puffy.

Preheat your oven to 350°F (175°C). Bake rolls for approximately 25 minutes, or until they are golden brown and cooked through.

While the rolls bake, beat together cream cheese and powdered sugar in a bowl until smooth. Once the rolls are warm from the oven, spread the frosting generously over the top before serving.