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Heat the oven to 350F (180C) and line the base and sides of a deep 10x10 inch (23x23 cm) square pan with parchment paper going in both directions, with the edges overhanging
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In a clean bowl, use a hand mixer to beat the egg whites with one third of the sugar until soft peaks form.
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In your stand mixer (or another bowl with a hand mixer), beat the remaining sugar with the butter, egg yolks and vanilla extract for about 3 minutes until pale and fluffy.
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In a medium sized bowl, use a whisk to blend the flour, cornflour and baking powder together. Adding one third of this at a time, beat into the butter and egg yolk mixture, alternating with the milk, until smooth.
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Whisk one third of the meringue into the batter to loosen it, then carefully fold in the remaining meringue until fully incorporated, do not overmix.
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Scrape the batter into the prepared pan and bake until golden and a toothpick inserted into the centre comes out clean or with a few moist crumbs. This should take about 45-55 minutes.
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Leave it to cool in the pan set on a cooling rack for a couple of minutes, then turn out onto the rack and leave until completely cold.
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Once the cake is completely cold, use a sharp serrated knife to level the top and trim the edges so that they are straight. Slice the cake into 20 evenly sized squares. I do this by slicing the cake into 4 equal strips. Take each strip and cut it into 5 pieces. The colder it is, the less crumbs you will get when slicing.
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You can do this the day before assembling. Store in the fridge.