Preheat the oven to 180C (350F). Lightly grease two 23cm (9-inch) spring-form cake tins with melted butter. Line the bottom of each tin with parchment paper. Butter the paper and then dust the tin with flour.
Sift the flour, baking powder, bicarbonate of soda, spices and salt in a bowl and set aside.
Separate two of the eggs.
In the mixing bowl of an electric mixer, beat together the oil and the sugar. Slowly add the whole eggs and the egg yolks, beating well. Add the carrots, and then add the walnuts. Then add the flour followed by the hot water. Beat the egg whites until soft peaks form and fold them into the cake batter.
Divide the cake mixture between the prepared tins. Place the baking tins on a baking tray in the middle of the oven and bake for approximately 45 minutes or until a skewer inserted into the middle of a cake comes out clean. Let cool for 10 minutes and then remove them from the tray and let cool on a baking rack.
For the icing:
Whisk all of the ingredients together in a bowl until light and fluffy. Cover with clingfilm and chill for 1-2 hours, until you are ready to ice the cake.
With a palette knife, spread a layer of icing on one cake, then press the other on top. Spread the rest of the icing over the top and sides of the cake. Refrigerate for at least 2 hours before serving. Keep refrigerated.