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.
Bring your eggs to room temperature so they will be easy to fold into the cake batter. To do this quickly, place them in a bowl and cover with warm (not hot) water. Let sit for 5-10 minutes, then remove and dry.
Make the Batter
In a large heatproof bowl set over 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.
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.
In the bowl of a stand mixer fitted with the whip attachment, whip the egg whites on medium-high speed until foamy, about 1-2 minutes. Slowly add the remaining ¼ 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.
Bake
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 room temperature or slightly warmer.
Serve
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.
Serve with toppings of your choice.
Notes
Ingredient Subs:
In place of hazelnut flour (aka hazelnut meal), feel free to use almond flour, almond meal, ground hazelnuts (toasted or not), or other ground nuts such as pecans or walnuts.
To make the cake dairy-free, use vegan butter and omit the salt if the butter is salty.
It's fine to use coconut sugar for the cake batter, but it's best to use granulated sugar for whipping the whites.
Make Ahead:
The cake can be baked 1-2 days before serving. Store covered at cool room temperature or in the fridge (but bring to room temp before serving)
The cake can be covered and frozen for up to 1 month. Defrost before serving.
Leftovers keep beautifully for up to 5 days in the fridge, or frozen for up to 1 month.