Position racks in the upper and lower thirds of the oven and preheat to 325 degrees F. Spread the hazelnuts on a baking sheet and bake until toasted, 12 to 15 minutes; let cool completely. Combine 1 cup each hazelnuts and sugar and the potato starch in a blender or food processor and pulse until very finely ground. Transfer to a large bowl.
Reduce the oven temperature to 275 degrees F. Line 2 large baking sheets with parchment paper. Using a bowl as a guide, draw three 7-inch circles on the parchment with a pencil (2 circles on 1 piece and 1 circle on the other); flip the parchment so the markings face down.
Put the egg whites, 1/2 cup sugar and the salt in a large heatproof bowl. Set over a saucepan of simmering water (do not let the bowl touch the water) and whisk until the sugar is dissolved and the mixture is warm, 2 to 5 minutes. Remove the bowl from the saucepan and beat with a mixer on medium-high speed until stiff and shiny but not dry, about 2 minutes.
Fold the milk and one-quarter of the egg white mixture into the nut mixture with a rubber spatula until smooth, then fold in the remaining egg whites until just combined. Divide the batter among the 3 circles on the parchment and spread evenly with an offset spatula to fill the circles. Bake 1 hour, 30 minutes, then switch the position of the pans and continue baking until firm, dry and golden, 1 to 2 more hours. (The layers are done when they easily peel off the parchment.) Let cool slightly on the baking sheets; peel off the parchment and transfer to a rack to cool completely.
Meanwhile, make the ganache: Put 1 cup cream in a microwave-safe bowl; microwave until very hot, about 2 minutes. Whisk in the chocolate and espresso powder until smooth. Let cool to room temperature, then cover and refrigerate until cold, thick and spreadable, at least 30 minutes. Make the whipped cream: Combine the remaining 4 cups cream and 1/3 cup sugar in a large bowl and beat with a mixer on medium speed until it barely holds soft peaks, 1 to 2 minutes. Finish beating the cream by hand with a whisk until soft peaks form; do not overbeat.
Put 2 meringue layers on a baking sheet; spread half of the ganache on each, to the edge. Refrigerate until set, 15 minutes. (If the ganache is too firm to spread, microwave in 20-second intervals to soften.) Place one of the ganache-topped meringues on a platter. Spread with 1 cup whipped cream. Stack the other ganache-topped meringue on top; spread with another layer of whipped cream. Top with the last meringue, then cover the top and side of the cake with the remaining whipped cream. Chop the remaining 1/3 cup hazelnuts and sprinkle on top of the cake along with the shaved chocolate. Refrigerate at least 6 hours or overnight before serving.