Prepare the Apples: Peel (optional), core, and chop the apples into small chunks. Toss with sugar, cinnamon, and nutmeg, and set aside.
Make the Cake Batter: Cream together the softened butter and sugar until light and fluffy. Beat in the eggs one at a time, then gently fold in the flour. Add a little milk if the batter is too thick.
Assemble the Cake: Grease and line a springform cake tin. Spoon half the cake batter into the tin, then layer the apple filling evenly over the top. Spoon the remaining batter over the apples.
Make the Crumble: In a separate bowl, rub together the flour, sugar, and cold butter with your fingertips until the mixture resembles breadcrumbs.
Add Crumble: Sprinkle the crumble mixture over the cake batter
Bake the Cake: Bake in a preheated oven at 180°C (350°F) for 45-50 minutes, or until a skewer inserted into the center comes out clean.
Cool and Serve: Let the cake cool in the tin for 10-15 minutes before removing it and placing it on a wire rack to cool completely. Serve warm with custard, or cold with cream. Dust with icing sugar or cinnamon if desired.