In a large bowl, combine the warm milk and yeast and let sit for 5–10 minutes until foamy.
Whisk in the granulated sugar, eggs, melted butter, vanilla bean paste, and white vinegar until smooth.
Add the cocoa powder, 2 1/2 cups of the flour, salt, and red food coloring, and mix until a soft dough forms.
Add the remaining flour a little at a time and knead for 5–7 minutes, until the dough is smooth, elastic, and only slightly sticky.
Place the dough in a lightly greased bowl, cover, and let rise in a warm place for about 1 hour, or until doubled in size.
In a small bowl, stir together the brown sugar and cinnamon for the filling and set aside; ensure the softened butter for the filling is spreadable.
Gently punch down the risen dough and turn it out onto a lightly floured surface.
Roll the dough into a 16×21-inch rectangle with the long side facing you.
Spread the softened butter for the filling evenly over the dough, leaving a small border on the edges.
Sprinkle the brown sugar and cinnamon mixture evenly over the buttered dough, pressing it lightly into the surface.
Starting from the long edge, roll the dough up tightly into a log, pinching the seam to seal.
Cut the log into 12 equal pieces and place them, cut side up, in a greased 9×13-inch baking dish.
Cover the dish and let the rolls rise for 30 minutes, or until puffy and touching.
Preheat the oven to 350°F while the rolls finish rising.
Bake the rolls for 20–25 minutes, or until the centers are cooked through and the edges are lightly golden.
While the rolls bake, beat together the cream cheese and softened butter for the icing until smooth and creamy.
Add the powdered sugar and vanilla bean paste to the cream cheese mixture and beat until fully combined.
Add the milk gradually and mix until the icing is smooth and spreadable.
Remove the baked rolls from the oven and let cool for 10 minutes.
Spread the cream cheese icing over the warm rolls and serve.