Warm the milk to about 110°F, then add the yeast and a teaspoon of sugar. Let it sit for about five minutes until it becomes foamy.
In a large mixing bowl, combine flour, sugar, salt, cocoa powder, and red food coloring. Add in the yeast mixture along with softened butter, egg, and buttermilk. Mix until a soft dough forms.
Knead the dough on a lightly floured surface for about seven to eight minutes until smooth and elastic.
Place your kneaded dough in a greased bowl and cover it with a clean towel. Let it rise in a warm place for approximately one hour or until doubled in size.
While waiting for the dough to rise, mix together brown sugar, granulated sugar, cocoa powder, and cinnamon in a small bowl.
Once your dough has risen beautifully, punch it down gently to release air pockets. Roll it out into a rectangle about twelve by sixteen inches on a floured surface. Spread softened butter evenly across this rectangle before sprinkling on your cinnamon-sugar filling mixture.
Starting from one long edge of your rectangle, roll up the dough tightly into a log shape. Use either a sharp knife or unflavored dental floss to cut it into twelve equal slices.
Arrange these slices in a greased nine by thirteen-inch baking dish with some space between each roll. Cover them again and let them rise for another thirty to forty minutes until puffy.
Preheat your oven to 350°F (175°C). Bake those lovely rolls for twenty to twenty-five minutes until golden on top and cooked through.
While baking, whisk together powdered sugar, milk, and vanilla extract until smooth. Adjust consistency by adding more milk if you'd like it thinner or more powdered sugar if you prefer it thicker.
Once out of the oven and slightly cooled, drizzle your warm rolls generously with that sweet glaze you've just made. Serve immediately while they're still warm and soft.