Preheat the oven to 340°F (170°C) and line a 9-inch (22 cm) cake pan with parchment paper.
Beat the egg whites until stiff peaks form, gradually adding the powdered sugar.
Gently fold in the ground walnuts and vanilla extract, then divide the mixture into 5 equal portions.
Bake each layer for 12-15 minutes, then let them cool completely.
Prepare the cream: cream the butter until light and fluffy, then mix it with the whipped cream and vanilla-flavored powdered sugar.
Layer the cake layers with the cream, and cover the top and sides of the cake as well.
Melt the dark chocolate, and prepare the glaze by making a syrup from the sugar and water.
Drizzle the glaze over the top of the cake and draw stripes through it with the melted chocolate to create the classic Eszterházy pattern.
Refrigerate the cake for at least 2 hours before serving to allow the flavors to meld.
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