Preheat oven to 350 degrees. Lightly spray (or grease) two small 8.5" x 4.5" loaf pans and set aside.
In a medium mixing bowl, whisk together the flour, baking powder, baking soda, cinnamon, nutmeg, cloves and salt.
In a large mixing bowl whisk together the brown sugar and granulated sugar, vegetable oil, eggs and vanilla extract. Break up any clumps of brown sugar and whisk until smooth.
Add the crushed pineapple with juice, and the grated carrots. Blend together using a spatula.
Add the flour mixture and fold together just until combined.
Divide the batter between the two prepared pans. Bake for 35-40 minutes. Check using a toothpick inserted into the center of the cake. Moist crumbs are okay but it should not come out wet.
Cool for 30 minutes in the pan, then remove to a wire rack to cool completely before icing.