In an electric mixer, combine warm milk, brown sugar, and yeast. Let it sit until bubbles form on the top.
Add salt, vanilla extract, butter, eggs, and flour to the mixer. Use the hook attachment to knead the dough until it's no longer sticky.
Cover the bowl and let the dough rise for 1 hour until doubled in size.
Prepare the filling by mixing brown sugar, coconut sugar, softened butter, and cinnamon.
Roll out the dough on a floured surface, spread on the filling, and roll it into a log.
Cut the log into individual pieces and place them in a buttered baking dish. Let them rise for 30 minutes.
Preheat the oven to 350°F and bake the rolls for 25 minutes.
While the rolls bake, prepare the frosting by mixing all the ingredients in an electric mixer.
Pour the frosting over the warm cinnamon rolls and enjoy the heavenly aroma!