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Position a rack in the center of the oven and preheat to 350ºF. Butter a 9-inch springform pan and line the bottom with a round of parchment paper.
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Make the cake: In a large heatproof bowl set over but not touching a pot of barely simmering water, combine the butter and chocolate. Stir occasionally until the mixture is nearly melted and smooth, about 5 minutes. Remove from the heat and stir until completely melted and smooth.
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In a medium bowl, whisk together ½ cup of the sugar, the hazelnut flour, and the salt to eliminate lumps. Whisk the hazelnut flour mixture into the chocolate mixture, then add the vanilla and finally the egg yolks.
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In the bowl of a stand mixer fitted with the whip attachment, whip the egg whites on medium-high speed until foamy, 1 to 2 minutes. Slowly add the remaining 1/4 cup sugar and continue whipping until the whites just hold soft peaks (when you pull the whip out and turn it upside down, the egg whites should form a peak that flops over). Don’t overwhip or the whites will be difficult to incorporate into the batter and will make a denser cake. Stir one-third of the egg whites into the chocolate mixture until just combined, then gently fold in the remaining two-thirds until no streaks remain.
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Scrape the batter into the prepared pan, smooth the top, and bake until puffed and cracked and the center is firm, 35 to 40 minutes. Let cool to about room temperature.
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Make the topping: Chill the bowl of a stand mixer in the refrigerator. Once cool, add the mascarpone, cream, sugar, and vanilla. Fit the stand mixer with the whip attachment and whip on medium-high speed until the mixture holds firm peaks. Chill until needed.
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When the cake is cool, release the sides of the pan, slide the cake onto a cutting board, and slice into wedges using a sharp chef’s knife dipped in hot water and wiped clean between each cut.
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Top each slice with the whipped mascarpone mixture and a sprinkle of pomegranate seeds.