Preheat the oven to 375°. Butter an 11 1/2-by-17-inch jellyroll pan and line the bottom with parchment paper. Butter the parchment. In a food processor, finely grind the hazelnuts. In a medium bowl, combine the ground hazelnuts with the flour and cinnamon.
In a large bowl, using a handheld electric mixer, beat the egg yolks with 1/2 cup of the sugar at high speed until light yellow, about 3 minutes.
In another large bowl, using clean beaters, beat the egg whites with a pinch of salt with the electric mixer at high speed until soft peaks form. Gradually add the remaining 1/4 cup of sugar and beat at high speed until the egg whites are firm and glossy.
With a large spatula, fold one-fourth of the dry ingredients into the egg yolk mixture. Fold in one-third of the beaten egg whites. Working in 2 batches, fold in the remaining dry ingredients and egg whites. Fold in the melted butter until just incorporated. Scrape the batter into the prepared jelly-roll pan and smooth the surface.
Bake for 10 minutes, or until the cake is golden and springs back when lightly touched. Let cool. Using the edges of the parchment paper, lift the cake out of the jelly-roll pan. Trim the edges and cut the cake into four 4 1/2-by-8 1/2-inch rectangles.
Line each of two 9-by-5-inch glass loaf pans with a cake rectangle. In a small bowl, mix the maple syrup with the Armagnac until blended; brush half of the syrup on the cakes in the loaf pans. Reserve the remaining syrup and cover the 2 remaining cake rectangles with plastic wrap.
Prepare an ice water bath in a medium bowl. In a small saucepan, combine the sugar and water and bring to a boil. Simmer over moderately high heat until the sugar syrup reaches 220° on a candy thermometer, about 8 minutes.
In a heatproof medium bowl, beat the egg yolks with a handheld electric mixer until light yellow, about 3 minutes. While beating the yolks at high speed, carefully and slowly pour in the hot sugar syrup; the mixture will thicken. Set the bowl in the ice water bath and beat the egg yolk mixture until chilled and very thick, about 4 minutes.
In large bowl, whip the cream to stiff peaks. Fold in the Armagnac and vanilla. Fold in the egg yolk mixture. Fold in the hazelnuts and chopped chocolate. Scrape the mousse into the loaf pans.
Brush one side of the remaining 2 cake rectangles with the remaining maple-Armagnac syrup; set them, brushed side down, over the mousse. Cover with plastic and freeze overnight or for up to 5 days.
To serve, fill a large bowl with 4 inches of very hot water and dip the bottoms of the loaf pans in the water for 10 seconds. Invert the cakes onto platters. With a sharp knife, slice the cakes crosswise 1 inch thick and transfer to plates. Drizzle the slices with the melted chocolate and serve.
The cakes can be frozen for up to 1 week.
An intense Armagnac with hints of vanilla and toffee will echo similar flavors in the mousse, while its high alcohol will balance the cake's sweetness.
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