Preheat the oven to 170°C, gas mark 3. Grease and line a 24-25cm-diameter springform springform cake tin.
Sieve the flour, baking powder, bicarbonate of soda, spices and salt into a large bowl. Whisk the eggs and oil together lightly. Add to the dry ingredients and mix well. Stir in the hot water then the sugar. Fold in the carrots, walnuts and pineapple.
Spoon into the tin. Bake for 1 hour, or until a skewer comes out clean. Cool for 10 minutes then release from the tin and cool on a rack.
For the topping, beat the butter and sugar together till smooth, add the vanilla, then beat in the cream cheese. Spread over the cold cake. Sprinkle with the coconut, if using, and serve.
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