Preheat oven to 350ºF. Grease and flour a 9" x 13" baking pan.
Mix first three ingredients together and beat for approximately two minutes. Blend the dry ingredients (the flour, baking powder, allspice and salt) well and add to the egg mixture. Add the pineapple and carrots and stir by hand to incorporate it all.
Pour the mixture into the pan and bake for 40-45 minutes or until a toothpick inserted in center comes out clean. Let cool thoroughly before icing. Use your favorite icing but add a little mint extract.