Preheat the oven to 190 degrees C. Grease a 23cm springform cake tin and sprinkle with breadcrumbs.
Place the grated carrots in a bowl and pour brandy over top; set aside.
Separate the eggs then mix the egg yolks with the sugar and salt until smooth.
Mix the flour, baking powder, almonds and carrots soaked in brandy into the egg and sugar mixture.
Whisk egg whites until stiff then fold in.
Tip cake mixture into prepared springform tin and bake in the preheated oven for 50-60 minutes. Cook in the tin before removing the springform rim.
Icing: Combine sugar with rum and lemon juice; stir until smooth. To adjust consistency add more icing sugar or liquid as needed. Spread the icing over the cooled cake and top with marzipan carrots, if desired.