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Preheat the oven to 350.
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Butter and flour a 9-by-2-inch round cake pan.
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In a small bowl, sift together the flour, baking powder and salt.
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Whisk to combine.
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In the bowl of a standing electric mixer, whisk together the eggs, egg yolks and granulated sugar.
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Set the bowl over a saucepan of barely simmering water; don't let the bottom of the bowl touch the water.
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Whisk vigorously until the mixture is warm to the touch.
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Return the bowl to the mixer and beat at medium high speed for 2 minutes.
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Add the vanilla and continue beating until the mixture is the consistency of whipped cream, 2 to 3 minutes longer.
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Meanwhile, in a small saucepan, melt the butter in the milk; do not boil.
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Remove from the heat; whisk.
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Sift one-third of the dry ingredients over the whipped eggs and gently fold in.
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Repeat this procedure twice.
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Pour the warm milk into the batter in a slow stream and continue folding until just incorporated.
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Scrape the batter into the prepared pan and bake for about 30 minutes, or until a tester inserted in the center comes out clean.
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Cool in the pan on a rack for 2 minutes, then turn the cake out to cool completely.
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Preheat the oven to 425.
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Spread the hazelnuts on a baking sheet and toast in the oven for about 8 minutes, or until fragrant.
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Wrap the hot nuts in a kitchen towel and vigorously rub them together to remove most of the skins.
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Let the nuts cool completely.
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Lower the oven temperature to 225.
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Line 2 large cookie sheets with parchment paper.
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Using the bottom of the 9-inch cake pan as a guide, trace two circles on one sheet of paper and a third on the other.
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In a food processor, finely grind the hazelnuts with the confectioners' sugar and cornstarch.
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Put the egg whites in the large bowl of a standing electric mixer and set it over a saucepan of barely simmering water; don't let the bottom of the bowl touch the water.
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Whisk the whites vigorously until warm to the touch; don't stop for even a few seconds or the whites will cook.
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Then beat the egg whites with the mixer at high speed until foamy.
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Add the cream of tartar and beat until soft peaks form.
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Add the superfine sugar, 1 tablespoon at a time, beating for 10 seconds between each addition.
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The meringue will be stiff and glossy.
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Using a large rubber spatula, gently fold the nut mixture into the whites.
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Scoop the meringue into a pastry bag fitted with a #5 open star tip (about 1/2 inch).
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Pipe a ring of meringue on one of the outlined circles on the cookie sheets 1/4 inch in from the perimeter.
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Then, starting in the center of the circle, pipe a continuous spiral to meet the outer ring.
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Fill in any holes with more meringue.
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It doesn't have to be perfect.
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Repeat to fill in the other two circles.
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Bake the meringues for 2 hours, or until dry and firm.
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39
Set aside 8 perfect strawberries.
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Slice the remaining berries 1/4 inch thick.
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Toss the berries in a bowl with the superfine sugar and vanilla.
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Set aside, stirring occasionally.
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In a small chilled bowl, whip the heavy cream with the confectioners' sugar until slightly firmer than soft peaks.
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Refrigerate until ready to use.
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Assemble the cake no more than 3 hours before serving.
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Split the sponge cake into 2 even layers.
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Invert the top layer onto a 9-inch cardboard cake round or serving platter.
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Drain the berries, reserving the juice.
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Using a pastry brush, dab half the juice on the cake layer.
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50
Evenly distribute half the sliced strawberries on the cake and spread 1 heaping cup of the whipped cream on top.
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51
Place a dacquoise disk over the cream and spread with 1/2 cup of the whipped cream.
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Repeat the layering with the second cake layer, the remaining berry juice and berries, another heaping cup of whipped cream and a second dacquoise disk.
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53
Using a serrated knife, quarter the remaining dacquoise disk, and then cut each quarter in half to get 8 wedges.
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If a wedge breaks, just glue it with a little whipped cream.
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Whisk the remaining whipped cream until it's stiff and transfer to a pastry bag fitted with the #5 star.
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Pipe 8 evenly spaced rosettes of whipped cream about 1/2 inch from the edge of the cake.
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Pipe 1 rosette in the center.
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Lay a reserved strawberry on each rosette and lean a wedge of the dacquoise against each berry with the point toward the center of the cake.
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To serve, slice with a serrated knife.