Preheat the oven to 175°C and grease or line an 8-inch square tin.
Combine grated carrots, beetroot, apple, beaten eggs, oil, and vanilla in a large bowl.
Sift the flour, baking powder, baking soda, salt, sugar, cinnamon, allspice, and nutmeg in a medium bowl.
Stir the dry ingredients into the wet ingredients until well mixed, then fold the walnuts.
Pour the cake mixture into the prepared pan and bake for approximately 40 minutes or until a toothpick inserted into the middle comes out clean. Invert onto a cooling rack and cool completely.
For the Spiced Glaze, mix icing sugar, softened butter, vanilla, milk (start with 1 tablespoon and add more as needed), and nutmeg until a thick glaze forms. Ensure it's not too thin.
Top Tip - Ensure the milk is at room temperature or the icing will split.
Spoon the icing over the completely cooled cake.
Optional: Garnish with additional chopped walnuts and dried hibiscus flowers.