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1
Preheat oven to 350F and butter a 10- by 2-inch round cake pan or 10-inch springform pan.
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2
Line bottom with a round of wax paper.
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3
Butter paper.
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4
Dust pan with flour, knocking out excess.
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5
Sift together 1 1/4 cups flour and 2 tablespoons sugar.
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6
Beat together yolks, 1 cups sugar, and warm water with an electric mixer until thick, pale, and doubled in volume, 5 to 7 minutes.
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7
Beat in vanilla, then gradually beat in flour on low speed until incorporated.
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8
Beat whites in a large bowl with cleaned beaters until they hold soft peaks.
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9
Add remaining 2 tablespoons sugar.
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10
Beat until whites just hold stiff peaks.
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11
Fold one third of whites into yolk mixture gently but thoroughly.
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12
Fold in remaining whites.
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13
Pour batter into cake pan and bake in middle of oven until pale golden and a tester inserted 1 inch from center comes out with a few crumbs adhering, 30 to 40 minutes.
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14
Turn off oven and cool cake in oven with door ajar 30 minutes.
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15
Run a knife around edge of cake and invert onto a rack.
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16
Remove pan and paper, then cool completely.
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17
Preheat oven to 350F.
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18
Toast hazelnuts in a baking pan in middle of oven until golden and skins are blistered, 10 to 15 minutes.
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19
Wrap nuts in a kitchen towel and let them steam 1 minute.
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20
Rub nuts in towel to remove loose skins (don't worry about skins that dont come off).
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21
Grind warm nuts in a food processor until they form a paste and chill until cold.
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22
Beat 2 cups cream with 5 tablespoons confectioners sugar with electric mixer until it holds stiff peaks.
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23
Chill until ready to assemble cake.
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24
Beat remaining cup cream with remaining 3 tablespoons confectioners sugar until cream just holds stiff peaks, then beat in cold hazelnut paste.
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25
Chill hazelnut filling until ready to assemble cake.
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26
Trim off any loose, crusty pieces from top and sides of cake.
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27
Halve cake horizontally with a long serrated knife and remove top half.
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28
Brush bottom half with two thirds of Strega, then spread all of hazelnut filling over it.
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29
Cover with top half of cake and brush with remaining Strega.
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30
Frost side and top of cake with whipped cream.
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31
Freeze cake until firm, at least 3 hours.
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32
Let cake stand at room temperature 1 hour before serving, then sprinkle top with chocolate shavings.
