Peel and core the apples and dice into approximately ½ inch cubes.
Melt the butter in a large skillet over medium heat, then add the apples, brown sugar and cinnamon.
Cook over medium heat, stirring occasionally, until apples have started to soften, about 10 minutes. Remove from heat.
While the apples are cooking, cut each cinnamon roll in half and form each half into a small ball.
Spray a 10-inch bundt pan with non-stick spray, add half of the dough balls to the bottom, then top with half of the apple mixture. Repeat with the remaining dough balls and apple mixture being sure to pour all the brown sugar liquid on top.
Place the bundt pan on the center rack of the oven and bake for 30 minutes until top is golden brown.
Once it is done baking, remove from oven and place on a cooling rack, allowing the bread to cool in the pan for about 20 minutes. Once you can handle the pan with your hands and the bread is only slightly warm, turn out the bread onto a platter or plate.
In a large bowl, beat cream cheese and butter until fluffy.
Add the powdered sugar a half cup at a time until well mixed.
With the mixer on low, slowly add the cream until the icing has thinned out and you can drizzle it. It should be about the consistency of liquid honey.
Optional: If you prefer, you can add more cream to make it more of a glaze or add less so that it is spreadable.
Drizzle the monkey bread with icing as desired and serve. Serve with additional icing on the side if desired.