Preheat oven to 350°F. Line an 8x8 inch baking pan with parchment paper, leaving some overhang on the sides to easily lift the bars out later.
Make the shortbread crust: In a large bowl, beat the butter and sugar together until light and fluffy, about 2-3 minutes. Beat in the vanilla and salt. Gradually mix in the flour until a dough forms. Press the dough evenly into the prepared baking pan.
Bake for 18-20 minutes, until lightly golden brown. Allow to cool completely.
Make the cheesecake filling: In a large bowl, beat the cream cheese with a hand mixer until smooth and creamy, about 2 minutes. Add in the sugar and vanilla and beat until combined. Then beat in the eggs one at a time, scraping down the sides as needed.
Pour the cheesecake filling over the cooled shortbread crust and spread it out evenly.
Make the spiced apples: In a medium skillet, melt the butter over medium heat. Add the diced apples, brown sugar, cinnamon and nutmeg. Cook for 5-7 minutes, stirring occasionally, until the apples are softened and the sauce has thickened slightly.
Spoon the warm spiced apples over the cheesecake filling, spreading them out in an even layer.
Refrigerate for at least 2 hours, or up to 5 days, before cutting into bars.
