In a large bowl, combine 2 cups flour, yeast, 1/2 cup sugar, salt, and cinnamon.
In a microwave save container combine the milk, water, butter, and cream cheese. Heat to 120 to 130 degrees F. Don't worry if the butter and cream cheese don't melt.
Add to the flour mixture along with the egg. Mix well with a wooden spoon.
Gradually add the rest of the flour until you have a soft dough. Mix this with your hand. Knead the dough until smooth and slightly sticky to your touch. Cover and let rise for an hour or until double in size.
Prepare the filling -
In a skillet add the butter, 4 tablespoons of sugar, 1 teaspoon cinnamon, and apples. Cook over medium heat until the apples are softened and caramelized. Set aside.
Once the dough is double in size, punch down the dough. Divide the dough into 24 equal parts. Roll each piece of dough and place it on a greased baking sheet. With your hand flatten the ball of dough.
Cover and let rise for 1/2 hour. With the tips of your fingers make a well in the middle of each bun.
Add a small scoop of caramelized apples.
Place the buns in a preheated 375 degree F oven and bake for 12 to 14 minutes or until lightly brownded. Remove from oven and cool completely on a cooling rack.
Drizzle with icing.
Prepare Icing -
Mix together the 3 cups of powdered sugar and cinnamon. Add enough cream to make the right consistency for drizzling over the cooled buns.