Line an aluminium cake mould by greasing with butter and dusting with refined flour.
Combine refined flour, salt, baking powder, all-spice powder, nutmeg powder, cinnamon powder and brown sugar in a bowl.
Break eggs in another bowl. Add vanilla essence, milk and butter. Blend with an electric blender till well mixed.
Add egg mixture to flour mixture and mix well till well blended.
Add 1½ cups grated carrots and mix well by cut and fold method till well blended.
Pour cake batter in lined mould filling ¾ and tap the mould. Put the mould in oven and bake at 180°C for 25-30 minutes.
To make cream cheese stuffing, take cream cheese in a bowl. Add powdered sugar and butter and whisk well. Add remaining grated carrots and walnuts and whisk well.
Remove cake from oven, demould and cool to room temperature.
Cut cake into slices. Spread a spoonful of cream cheese stuffing on one slice and cover with another slice to make a sandwich. Make other sandwiches in a similar way.
Stack sandwiches on top of one another and dust with icing sugar. Serve immediately.