In a large skillet over medium-low heat, melt butter. Add apple mixture and cook, stirring occasionally, until thickened and apples are slightly tender and coated with a caramel-like sauce, about 10 minutes. Remove from heat, transfer to a bowl, and allow to cool to room temperature. Drain the apples to remove the excess liquid.
In a large bowl, place the melted butter and brown sugar and whisk until well combined. Whisk in the egg and vanilla extract. Add flour mixture and fold, using a rubber spatula or wooden spoon, just until combined. Do not over mix. Fold in the drained apples.