Add the butter and sugar to a bowl and beat on medium with a paddle beater (or use handheld beaters) until combined. The butter should be mixed well and not lumpy.
Add egg and vanilla and mix for 30 seconds until the egg is just combined.
Add the baking powder and the flour in small increments. Scrape down the sides with a spatula to incorporate all ingredients.
Turn the dough onto a piece of plastic wrap, and shape it into a ball. Cover and refrigerate for 30 minutes.
Preheat oven to 180C/350F
Grease a 23cm/9inch round cake tin
Divide dough into equal halves.
Using lightly floured hands, press half of the dough into your greased pan as evenly as possible. Use your hands to work the dough to the edges.
Top with the apple pie filling.
Roll (or use your hands to press) the other half of the dough into a rough round that fits the size of the pan. Place the dough on top of the pie filling and use your hands to gently press the dough into any missing gaps.
Bake for 25-30 minutes in a fan-forced oven until browned on top.
Cool for 20 minutes in the tin, then turn out onto a wire rack and cool completely.
Transfer to a plate and serve with a dusting of icing sugar and some cream and/or ice cream.
Notes
Baking Accuracy - for the best results, use a digital kitchen scale to measure your ingredients in grams or pounds/ounces. Cups are not as accurate as American cup sizes differ to Australian cup sizes, which I use. Butter - your butter must be at room temperature for it to combine with the sugar. If you're short of time, microwave the butter for 10-20 seconds at a time until it's just soft. Self-Raising Flour - if you use self-raising flour, then add 225g and do not use the baking powder.Dividing the Dough - to weigh your dough evenly, you can use a set of kitchen scales. Otherwise, just eyeball the dough for an estimate. Cooling theCake - it doesn't matter so much if the top of the cake (before baking) is rough. Simply flip the cake onto a serving plate, and the top will become the bottom. Cool the cake completely before sifting over some icing sugar. Serving - serve warm with a dollop of thick cream or ice cream.