Sprinkle the yeast over the warm water and gently stir. Set aside to proof.
Place the cake mix, flour, and salt in the bowl of a stand mixer with the dough hook attachment and turn on for 10-15 seconds.
Pour in the yeast mixture and mix.
Add the beaten eggs and vanilla extract.
Knead the dough for 3-5 minutes until the dough begins to pull away from the side of the bowl.
Spray a large mixing bowl with cooking spray and place the red velvet dough in the bowl, turning once to coat.
Spray a square of plastic wrap, large enough to cover the bowl, and place it over the bowl to cover the dough.
Place the bowl in a dry, warm place and let the dough rise until double in size.
When the dough has risen, remove the plastic wrap and punch down the dough.
Place dough onto a lightly floured surface and sprinkle the top with flour.
Use a rolling pin to roll dough into a large rectangular shape.
Use a silicone spatula to gently spread softened butter over the rectangle.
Cover the top of the dough evenly with the brown sugar.
Sprinkle the cinnamon over the brown sugar.
Roll the dough up tightly starting with the long side of the dough.
To cut the rolls, gently slide a piece of unwaxed dental floss under the roll.
Find your desired place to cut (about two inch slices) and pull the two ends of the floss up over the roll and cross them. Pull them tight around the roll and the floss will cut through.
Place the rolls on a baking sheet lined with parchment paper and bake at 375° for 20-25 minutes.