Preheat your oven to 375°F (190°C). Grease an 8-inch round cake pan and line the bottom with parchment paper.
Place the hazelnuts on a baking sheet and roast them in the oven for about 10 minutes. Once roasted, transfer the nuts to a clean tea towel and rub them to remove most of the skins. Some skins may still remain, and that’s okay. Place the nuts in a food processor and grind them finely.
In a large mixing bowl, beat the softened butter and sugar together until light and fluffy.
Gradually add the egg yolks into the butter mixture, one at a time, beating well after each addition.
Stir the ground hazelnuts into the mixture. Dissolve the coffee granules in the warm milk, then stir this into the batter.
In another bowl, combine the flour, baking powder, and salt. Gradually add this dry mixture to the wet ingredients, mixing until just combined.
In a separate clean bowl, whisk the egg whites until soft peaks form. Gently fold the whipped egg whites into the batter, being careful not to deflate them.
Pour the batter into the prepared cake pan and level the surface with a spatula. Bake for 25 minutes, or until the cake is risen and springs back when lightly pressed.
Once the cake is done, let it cool in the pan for a few minutes. Then, turn it out onto a wire rack to cool completely.
While the cake cools, prepare the apple filling. In a saucepan, combine the sliced apples, apricot jam, and lemon zest and juice. Cook gently over low heat, covered, until the apples are soft but still hold their shape. Let the mixture cool to room temperature.
Once the cake is fully cooled, slice it horizontally in half using a serrated knife. Spread the cooled apple mixture evenly between the two layers, then carefully assemble the cake. Melt the dark chocolate in a heatproof bowl set over simmering water. Spread the melted chocolate over the top of the cake and allow it to set before slicing and serving.