Melt unsalted butter in a large skillet over medium heat.
Add the chopped apples and cook for 6-8 minutes, stirring frequently.
In a small bowl, blend water and cornstarch, then pour this mixture over the apples.
Add light brown sugar and ground cinnamon to the skillet, stirring continuously. Allow the mixture to reach a slight boil and cook for an additional 2-3 minutes.
Stir in vanilla extract and remove from heat.
Let the apple mixture cool for 5 minutes before pouring over the prepared cheesecake.