To make the crumble topping, combine all the ingredients in a bowl and set aside.
Using an electric mixer, beat the butter and sugar together until light and fluffy, then add the egg yolks, one at a time, beating well after each addition. Continue to beat for a further 3 minutes, or until creamy. Fold in the sifted flour, cinnamon, cardamom and baking powder and then stir in the almond meal.
Using an electric mixer, whisk the egg whites in a clean, small bowl until they form stiff peaks. Gently fold the egg white into the cake batter in two batches. Fold the chopped apple through the batter. Spoon the batter into the prepared tin and smooth the surface. Sprinkle the crumble mixture over the top.
Cover the top of the cake with a piece of foil and