In a large mixing bowl, combine the red velvet cake mix, 1 cup of flour, and yeast. Add warm water and beat on medium speed for 2 minutes until smooth.
Gradually stir in enough of the remaining flour to form a soft dough (the dough will be sticky).
Turn the dough onto a lightly floured surface and knead gently 6-8 times. Place the dough in a greased bowl, turning once to grease the top. Cover and let it rise in a warm place until doubled, about 2 hours.
While the dough rises, mix the brown sugar and cinnamon in a separate bowl.
Once the dough has risen, punch it down and turn it onto a lightly floured surface. Roll the dough into an 18×10-inch rectangle.
Brush the dough with melted butter, leaving a ¼-inch border around the edges. Sprinkle the cinnamon-sugar mixture evenly over the buttered dough.
Starting with the long side, roll up the dough jelly-roll style. Pinch the seam to seal. Cut the roll crosswise into 12 equal slices.
Place the slices, cut sides up, into a greased 13×9-inch baking pan. Cover with a kitchen towel and let them rise in a warm place until almost doubled, about 1 hour.
Preheat the oven to 350°F (175°C). Bake the rolls for 15-20 minutes or until puffed and light golden brown. Allow the rolls to cool slightly.
For the Icing:
In a mixing bowl, beat together the confectioners’ sugar, softened butter, vanilla extract, and enough milk to reach a drizzling consistency.
Drizzle the icing over the warm cinnamon rolls and serve.