Pre-heat the oven to 200°C.
Roll the pastry out to 1cm thickness on a lightly floured surface and cut rounds that will fill 4 x 8cm straight-sided tartlet tins. Line the tins with the pastry, pressing in well around the edges and prick the bases with a fork. Line with nonstick baking paper and baking beans. Blind bake on a baking sheet for 12-15 minutes until the edges just start to colour. Remove from the oven and discard the baking paper and baking beans.
Reduce the oven to 180°C.
Allow to cool in the tins on a wire rack while you prepare the filling. Cream together the butter and sugar using an electric hand held whisk until pale and fluffy, then gradually beat in the eggs, mixing well between additions. Fold in the ground almonds.
Spread the bases of the pastry cases evenly with the almond paste filling. Arrange the slices of apple overlapping across the middle of the tartlets, going from one edge to the other. Return to the oven on baking trays for 20-25 minutes until the filling is cooked and the apples are coloured on top. Remove and allow to cool a little before turning out from the moulds and serving.
*This tartlet is very rich and indulgent, so it shouldn't be eaten too often. But it's perfect for those special occasions!