Place yeast and sugar into stand mixer then add warm water and gently stir. Let sit until yeast has doubled, about 10 minutes. In a medium bowl, mix melted butter and warm milk. Add butter and milk mixture to yeast mixture with the dough hook attachment on low speed then add sugar and egg mixing until combined. In a large bowl, stir together the flour and salt. Add 2 cups of flour mixture to the mixer at a time scraping sides of bowl, continuing to add remaining flour until the dough starts to clean sides of mixing bowl. Kneed dough on low speed for 7 minutes. Place dough onto a floured counter and dived dough in half. Place one half of the dough back in the mixing bowl and add 6-8 drops of red food coloring. kneed dough until the dough is solid red (in my case pink :( ) and you see no streaks of red. Place dough into a large bowl that has been sprayed with cooking spray, spray another bowl and place the non-colored dough in this bowl. Cover each with a damp cloth and let rise in a warm place for 45-60 minutes, until dough doubles in size.
Remove each dough from the bowl and place onto a floured counter top. With a floured rolling pin, roll each dough into an about 7×9.5 inch rectangle, about 1/4 inch in thickness. Spread softened butter over entire surface of each dough (half a stick each). In a medium mixing bowl, stir together the brown sugar, sugar and cinnamon. Sprinkle evenly over both buttered doughs. Using a pizza cutter or sharp knife carefully cut 14 1 inch wide strips from each dough. Working with one strip at a time fold the strip in half and pinch the edges to seal (you are trying to enclose the filling). Repeat with remaining strips. You should now have 12 white and 12 red ropes. If you want to make small candy canes cut each rope in half. Pinch the ends together to seal.
Spray 2 baking sheets with non-stick spray.
Take one red and white white rope and pinch the tops together. Twist one rope around the other and seal the ends together. Place on baking pan and shape the long twist into a candy cane. Repeat with remaining twist. Sprinkle the cinnamon sugar that fell onto the counter all over the candy canes.
Cover both pans and allow to rise in a warm place for 45-60 minutes or until rolls have doubled in size. When rolls are ready reheat oven to 350 degrees F. Bake rolls for 15-17 minutes or until rolls are golden brown and baked through. Set aside to cool slightly.
For the glaze, mix together the powdered sugar, milk and vanilla extract. If glaze seems too runny, add a little more powdered sugar. Place glaze in a small plastic bag and snip the tip off. Drizzle lines back on forth over the candy canes. Serve