Photograph: Karen Thomas
Preheat the oven to 200°C, fan 180°C, gas 6. Line the sides and removable base of a 23cm round cake tin with baking paper.
Finely grate the lemons and place the zest in a mixing bowl with 2 tablespoons of lemon juice. Set aside 2 tablespoons of lemon juice for the icing. Finely grate the carrots. Mix into the lemon zest and juice, and set aside.
Sift the flour, baking powder and a pinch of salt into a bowl. Roughly crush the cardamom pods with a pestle and mortar or under a rolling pin. Remove the little black seeds and grind them into a powder. Mix into the flour with the ground almonds.
Place the egg whites in a large dry bowl. Whisk until they form soft peaks. Add 2 tablespoons of caster sugar and continue to whisk, gradually adding the remaining sugar until it is all used and the egg white forms a glossy, floppy meringue.
Roughly beat the egg yolks. Fold them into the egg whites with a metal spoon, followed by one-third of the almond flour mixture, then one-third of the carrots – you'll need to separate out the grated carrots and sprinkle them over the mixture. Repeat until all the ingredients are mixed into the meringue. Pour into the prepared cake tin and bake in the middle of the preheated oven for about 30 minutes, or until the cake springs back when pressed and an inserted skewer comes out clean.
Remove from the oven. Once cold, remove the cake from the baking tin and peel off the paper.
To make the lemon icing, sift the icing sugar into a bowl. Using a wooden spoon, stir in the lemon juice, followed by the orange flower water, until you have a thick, smooth icing. Spread the icing all over the cake, using a wet knife, if necessary. Once the icing begins to set, press in eight blanched almonds around the edge.
This recipe is adapted from The Great British Vegetable Cookbook by Sybil Kapoor (£25, National Trust Books)