Bake the hazelnut layers:

1. Preheat oven to 170 °C / 340 °F (top/bottom heat).
2. Beat egg whites with a pinch of salt until stiff peaks form. Gradually add sugar while beating until the meringue is glossy and firm.
3. Mix hazelnuts and sifted flour, then gently fold into the meringue with a spatula – do not overmix.
4. Spread the batter into 5 circles (22–24 cm / ~9 inches) on parchment-lined baking sheets.
5. Bake each layer for 10–12 minutes until set and lightly golden. Remove and cool completely.

Prepare pastry cream & hazelnut buttercream:

1. In a bowl, whisk egg yolks with sugar, cornstarch, and vanilla.
2. Heat milk in a saucepan until steaming. Slowly pour into the egg mixture while whisking constantly.
3. Return everything to the pot and cook over medium heat, stirring constantly, until thickened.
4. Strain through a sieve, cover with plastic wrap (touching the surface), and let cool completely at room temperature.
5. Whip butter for 5–8 minutes until very pale and fluffy.
6. Gradually add the cooled pastry cream, one spoonful at a time. Beat well.
7. Fold in hazelnut paste (and rum if using), then whip again for 1–2 more minutes until smooth and airy.

Assemble the cake:

1. Place the first cake layer on a serving plate. Spread a layer of buttercream over it.
2. Repeat with remaining layers, stacking carefully. Do not frost the top layer – it will be glazed.
3. Spread a thin layer of buttercream around the sides and press toasted sliced almonds onto the edge.

Glaze and decorate:

1. Cut white fondant into small chunks and warm gently with hot (not boiling) water, stirring until smooth and pourable.
2. Pour fondant onto the top of the cake and spread evenly with a palette knife.
3. Pipe melted chocolate in spirals or lines. Use a toothpick to draw alternating lines through the chocolate (in and out) to create the classic Esterházy web pattern.
4. Chill for at least 3 hours – best overnight.