Preheat the oven to 400 degrees F. Spray a 9x13-inch baking pan with nonstick spray.
PREPARE THE APPLE FILLING:
In a medium skillet, melt the butter over medium heat. Add the apples and sugars. Saute until the apples are slightly softened, about 5 minutes. Set aside to cool.
PREPARE THE CINNAMON- SUGAR FILLING:
In a medium bowl, add the filling ingredients (brown sugar, butter and cinnamon) and stir until the mixture is combined and lumpy.
PREPARE THE CINNAMON ROLL DOUGH:
In a medium bowl, whisk together the flour, sugar, baking powder and salt. In a separate bowl, use a whisk to combine the applesauce, milk, butter and egg. Add the wet mixture to the dry ingredients and use a wooden spoon to combine until well mixed. Remove the dough to a well-floured surface, sprinkling in more flour as needed to make sure the dough isn't sticky. Roll the dough out into a (roughly) 12x8-inch rectangle. Sprinkle the dough with the cinnamon-sugar mixture, then the cooled apples. Roll up the dough log-style. Cut 1-inch slices and carefully place them in the prepared dish, leaving a little bit of space between each roll. Bake 20 to 25 minutes, or until the rolls are a nice golden brown.
PREPARE THE ICING:
In a medium bowl, whisk together the icing ingredients until smooth. Spoon the icing over the warm rolls. Serve warm. Leftovers may be stored in a covered container and enjoyed later.