Preheat the oven to 180°C/Gas Mark 4. Grease and line a 23cm (9in) square cake tin with baking paper, using a little butter.
Melt the remaining butter in a large saucepan over a low heat, without letting it get too hot. Remove from the heat, then add the orange juice and beaten eggs. Reserve the orange zest for the frosting.
Sift together the flour, salt, bicarbonate of soda, baking powder and ground ginger in a mixing bowl. Stir in the sugar, organic carrots and courgettes, then add the melted mixture and stir together well.
Turn the mixture into the prepared tin and bake for 45-50 minutes, or until a fine skewer inserted into the centre of the cake comes out clean. Cool in the tin for 20 minutes, then turn out carefully. Cool completely on a wire rack.
Make the frosting by beating the low-fat soft cheese, vanilla extract and reserved orange zest together. Spread on top of the cooled cake. Put the grated organic carrot into a frying pan with the sugar and heat gently to melt and caramelise. Cool, then scatter over the cake.