Adapted From Martha Stewart. Mine uses cream cheese, not goat cheese, frosting.
In a medium sauce pan, spread 1/3 cup sugar in an even layer, cook over medium high hear, without stirring, until sugar begins to turn golden and melt around the edges (3-4 min). Using a wooden spoon, slowly stir until meted and mixture is a translucent golden amber.
Add apple chunks and lemon juice, and stir to coat apple pieces with caramel.
Cover and cook over low heat until apples fall apart, 6-8 minutes. Continue cooking, stirring frequently, until mixture reaches the consistency of applesauce and generously coats the back of the spoon, about 5 minutes more.
Remove from heat and cool completely.
(Don't think you can get away w/o rotating the pans... I did and ended up with lopsided layers)