Preheat your oven at 350 degrees Fahrenheit.
In a large bowl, sift the dry ingredients together (flour, allspice, cinnamon, baking powder, baking soda, and salt). Whisk until well combined and set aside.
Mix together the sugars (brown and granulated) with the eggs until well combined.
Gradually add the oil into the egg-sugar mixture while whisking continuously. Whisk until the oil is fully incorporated.
In small batches, fold the dry ingredients into the wet mixture with a spatula.
Once the flour is fully incorporated into the batter, add the shredded carrots and crushed pineapple.
Fold the carrots and pineapple into the batter until it is completely incorporated
Pour the batter into 3 8-inch round tins that are lined with parchment paper.
Bake the cake at 350 degrees Fahrenheit for 25-30 minutes.
Allow the cake to rest for at least one hour before icing and serving.