Line a 13 by 9 inch nonstick baking dish with parchment paper. Make sure the paper hangs over by two inches on all sides. Brush the paper with melted butter. Preheat the oven to 350 degrees.
In a mixing bowl sift together the flour, sugar, and salt. Stir in the butter, egg, and vanilla. Stir until a dough is formed. Remove a third of the dough and wrap it in plastic wrap and chill it. Press the rest of the dough evenly into the bottom of the pan. Cover the pan with plastic wrap and refrigerate while you make the apple filling.
For the Apple Filling: Melt the butter and sugar in a large skillet on medium heat. Add the apples, cinnamon , and nutmeg and cook, stirring occasionally, until the apples are tender and most of the liquid has evaporated. Take care not to burn the apples. This will take about twenty minutes.
Spread the apples evenly over the crust. Sprinkle on the walnuts.
On a floured board, roll out the rest of the dough and use a cookie cutter to cut out shapes. Place them all over the top of the bars. Bake for 40 minutes, and then cool on a wire rack. Cut into bars and serve.