How to Make It
Preheat the oven to 350°. Generously coat a 10-inch Bundt pan with nonstick cooking spray and dust it with cocoa powder.
Spread the hazelnuts on a rimmed baking sheet and toast for about 10 minutes, until golden and fragrant. Transfer the hazelnuts to a kitchen towel and let cool slightly, then rub off the skins. Let cool completely. In the bowl of a food processor, pulse the hazelnuts until they are very finely chopped and slightly powdery. Transfer the ground hazelnuts to a medium bowl and whisk in the flour and salt.
Sift the 2 cups of confectioners’ sugar into another medium bowl with the 3/4 cup of cocoa powder. In a standing mixer fitted with the paddle, beat the butter with the granulated sugar and brown sugar at medium speed until fluffy, about 2 minutes. Scrape down the side of the bowl. Reduce the speed to low and beat in the whole eggs and egg yolks, one at a time, until just incorporated. Add the vegetable oil and vanilla extract and beat until the batter is uniform in color, about 1 minute. Add the cocoa mixture and beat until incorporated. Using a spatula, gently fold in the hazelnut mixture until no streaks remain.
Scrape the batter into the prepared pan, smoothing the top. Bake the cake in the middle of the oven for 40 to 45 minutes, until it starts to pull away from the side of the pan and the top just springs back when you touch it; the center should still be soft. Let the cake cool on a rack for at least 2 hours; it may crack and sink slightly. Invert the cake onto a plate and dust with confectioners’ sugar. Cut the cake into wedges and serve.