Cook the pumpkin in a saucepan of boiling water for 15-20 minutes until soft and tender. Strain and allow to cool a little before pulsing in a food processor with a little of the buttermilk until smooth. Press the purée through a sieve and collect in a bowl below; cover and reserve to one side.
Preheat the oven to 190°C.
Grease and line a 7 inch springform square cake tin with nonstick baking paper. In a mixing bowl, combine the melted butter and remaining buttermilk and set to one side.
In a separate bowl, beat together the eggs, vanilla extract and sugar using an electric whisk until pale and fluffy. Combine the butter mixture with the egg mixture and mix well. Fold the flour and pumpkin purée into the mixture until smooth.
Spoon the mixture into the cake tin. Bake for 25-30 minutes until golden and risen. Remove and allow to cool in the tin for 10 minutes. Turn out from the tin and discard the nonstick baking paper; allow to cool on a wire rack until cold. Cut the cake so that you have three different sizes of square cake. Stack one on top of the other in order of size and serve.
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