Pour half of the batter into the prepared pan and spread into an even layer. Sprinkle half of the cinnamon-sugar mixture over the batter. Spoon the remaining batter into the pan. Sprinkle the rest of the cinnamon-sugar mixture over the top, making sure all the surface is covered.
Make the Cream Cheese Icing: With an electric mixer, beat the softened cream cheese and butter until fluffy. Carefully add the sugar. Beat until combined. Then add the cream or milk, mix until combined.