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Heat a dry frying pan over a medium heat and tip in the hazelnuts. Toast, shaking the pan from time to time, until golden and fragrant. Transfer to a plate to cool completely, then tip into a food processor and blitz until finely chopped, like breadcrumbs.
Oil and line the base and sides of a 23cm springform cake tin. Tip the chocolate into a heatproof bowl and set over a pan of simmering water, making sure the base of the bowl doesn’t touch the water. Melt the chocolate, giving it a stir every now and then. Alternatively, melt in short blasts in the microwave. Once fully melted, remove from the heat and slowly pour in the olive oil, whisking constantly
until smooth and glossy.
Beat the egg yolks and 50g of the caster sugar in another bowl until pale and thickened, around 5 mins. Gently fold the whisked yolk mixture into the chocolate mixture along with the chopped hazelnuts and a pinch of sea salt. (The ingredients don’t need to be fully combined yet.) Set aside.
Whisk the egg whites and the remaining sugar together in a separate bowl, using a stand mixer or an electric whisk, until medium soft peaks form. Use a large metal spoon to stir a little of the whites into the chocolate mixture to loosen, then gently fold in the remainder. Carefully pour the batter into the prepared tin. Will keep wrapped in the freezer for up to two months.
If not freezing the cake, heat the oven to 180C/160C fan/gas 4 and bake for 35-45 mins. To bake from frozen, heat the oven as above, but bake for 55-60 mins, until a skewer inserted into the middle comes out almost clean, with just a few crumbs clinging to it. Leave to cool in the tin until warm, then carefully remove the base and sides of the tin. Dust over the icing sugar and serve with scoops of vanilla ice cream, if you like.