Preheat oven to 350 degrees F. Lightly grease an 8x8-inch square pan.
In a large mixing bowl, whisk together the flour, sugar, baking powder and salt. Whisk in the egg, melted butter, milk and vanilla until moistened. Spread evenly in the pan (mixture will be slightly sticky).
Make the filling:
In a large bowl with an electric mixer, beat together the cream cheese and apple butter until smooth. Beat in the egg, then beat in the melted butter and vanilla. Scrape down the bowl, then beat in the powdered sugar, cinnamon and nutmeg.
Spread the filling over the cake layer, then bake 45-50 minutes or until the center is set (do not overbake as the center should be slightly gooey). Cool completely before serving. Garnish with whipped cream and dust with cinnamon. For best results, let cake sit at room temperature for 15-30 minutes before serving.
Refrigerate any leftovers in an airtight container for up to 4 days.