Cook the apples. In a medium skillet or saucepan over medium heat, melt the butter. Add the brown sugar and cinnamon and stir until combined. Add the diced apples and sauté for about 10 minutes, stirring occasionally, until the apples are just tender and starting to break down slightly.
Thicken. Sprinkle the cornstarch over the top, stir well, and cook for 1 more minute, until everything thickens up and looks glossy.
Cool completely. Set the filling aside to cool. It needs to be room temperature or cooler before it goes on the cheesecake layer, so make this first!