Pans needed: Medium-sied bowl for mixing carrots and pineapple, large bowl for mixing ingredients, medium-to-large bowl for mixing frosting. 9-by-13 inch baking pan.
This is a very moist cake, and it will likely stick to the bottom of your baking pan. You can avoid this by lining the bottom of the pan with parchment paper before adding the batter.
Preheat oven to 350 degrees F (175 degrees C). Grease a 9-by-13 inch baking pan, or a 12 inch cast iron skillet. Because the cake will likely stick, cut a sheet of baking parchment paper and cover the bottom of the pan. The pan needs to be greased before applying the paper, so the cake will pull away from the sides of the pan as it bakes.
Peel and grate carrots. Strain pineapple to remove most of the liquid. Mix drained pineapple into carrots.
In a large bowl, beat together eggs, oil, applesauce, white sugar and vanilla. Mix in flour, baking soda, baking powder, salt, and spices: cinnamon, nutmeg, ginger, cardamom. Stir in carrots-pineapple mixture. Fold in pecans. Pour into prepared pan.
Bake in the preheated oven for 40 to 50 minutes, or until a toothpick inserted into the center of the cake comes out clean. Let cool in pan for 15 minutes, then turn out onto a wire rack and cool completely.
This recipe for carrot cake gives a result that is very, very rich – so rich, in fact, that a typical frosting (such as the kind you buy at the store) may be a little more sweet than it needs to be. This quick and easy frosting recipe has been adjusted a bit more so that the coating will have more of a "cream cheese" flavor to blend with the cake.
In a medium-to-large bowl, combine butter, cream cheese, confectioners' sugar and vanilla. Beat until the mixture is smooth and creamy. Frost the cooled cake.