In a stand mixer bowl, combine cake mix, 1 cup flour, and yeast. Add warm water and mix on medium speed for 2 minutes.
Gradually add remaining flour until a soft, slightly sticky dough forms. Knead gently on a floured surface 6–8 times.
Place dough in a greased bowl, cover, and let rise in a warm area for about 2 hours or until doubled.
Mix brown sugar and cinnamon in a small bowl.
Roll dough into an 18×10-inch rectangle. Brush with melted butter and sprinkle evenly with cinnamon sugar.
Roll tightly from the long side and slice into 12 pieces.
Arrange rolls in a greased 13×9-inch pan. Cover and let rise for 1 hour.
Bake at 350°F (175°C) for 15–20 minutes until puffed and lightly golden.
Beat icing ingredients until smooth and drizzle over warm rolls. Serve immediately.