Preheat oven to 350°F.
Prepare a 9 inch round cake pan by thoroughly buttering the bottom and sides, then sprinkling it evenly with flour and tapping out the excess.
Sift together the flour, almonds, baking powder, cinnamon and salt. The ground almonds might not pass through your sifter. If not, just stir them into the flour mixture.
Peel and core the apples. Cut into quarters and then cut each quarter into three chunks.
In a mixer (or by hand if you wish) beat the eggs with the sugar and vanilla. Mix in the flour and then the melted and cooled butter. Stir in the apple chunks.
Pour into the prepared pan and bake at 350°F for 50 minutes or until a toothpick poked in the center comes out clean.
Remove from the oven and let cool for 10 minutes. Run a knife around the edge of the cake to release. Turn out onto serving dish. Serve warm.