Preheat the oven to 180C (350F) and prepare 2 round cake tins. Grease the cake tins with butter or spray with cooking oil.
In a large mixing bowl, add the all purpose flour, baking soda, salt and spices (cinnamon, nutmeg, ginger and all spice). Stir well to combine and set aside.
In another mixing bowl, combine the milk, eggs, brown sugar, vegetable oil, lemon juice and sourdough starter. Whisk well to combine and dissolve the sugar into all the other ingredients.
Now to the wet ingredients, add the grated carrot, pineapple, coconut and pecans. Whisk well to ensure all of these add ins are well distributed through the wet ingredients.
Now, pour the liquid ingredients onto the dry ingredients and stir together until the flour mixture is moistened and there are no big lumps or clumps of flour.
Pour the sourdough carrot cake batter evenly between the two round cake tin and place gently into the oven for around 50 minutes or until a toothpick comes out clean.
Remove from the oven and allow to cool in the pans for around 10 minutes before inverting onto a wire rack to cool.
When you're ready to frost the sourdough carrot cake, place all frosting ingredients into a food processor or stand mixer bowl and whip until smooth.
Place one half of the cake onto a plate and spread a generous amount of icing on top before placing the second cake on top. Use additional icing to cover the top and sides of the cake.