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Preheat the oven to 200°C (390°F) and grease a 20cm round cake tin and line the base and sides with baking paper. The paper should protrude about 2.5cm above the tin.Place the walnuts on a baking tray and cook for 4-5 minutes or until lightly roasted. Cool and cut into thirds.
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Sift the flour, baking powder, baking soda, spices and salt into a bowl. Repeat to ensure they are evenly mixed.Put the egg whites in a very clean bowl of an electric mixer fitted with the whisk attachment. Beat the egg whites on high speed until soft peaks start to form. Slowly pout in the sugar for the egg whites while the motor is still running and whisk until soft peaks form. Quickly transfer the meringue to another bowl and set aside until needed.
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Put the egg and egg yolk in the bowl of an electric mixer and add the sugar for egg yolks. Mix on high speed for 3-4 minutes or until the mixture doubles in volume and is quite airy. With the motor still running, slowly pour the oil in a thin stream being careful that it doesn’t split or deflate too much.Remove the bowl from the mixer and with a spatula, gently fold in the flour mixture until combined. Fold in the carrots and walnuts. Working quickly, lightly fold in the meringue, but do not fold in completely. You should still be able to see white streaks through the mixture.
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Pour into the prepared tin and bake for 1 hour and 10 minutes, or until a skewer inserted into the centre of the cake comes out clean. You may need to drop the oven temperature to 180°C (350°F) after the first 30 minutes if the top is browning too quickly.
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To make cream cheese icing, combine ingredients in the bowl of an electric mixer until smooth.
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Remove the cake from the oven and allow to cool in the tin for about 30 minutes before turning it onto a wire rack to cool completely. Using a serrated knife, slice horizontally through the centre of the cake to form two even-sized layers and fill with cream cheese frosting. Dust the top of the cake with icing sugar and serve.