Carrot cake is notoriously dense, so you honestly may not have done anything at all wrong. Some recipes I've found are denser than others.
Simple Carrot or Apple or Zucchini Cake
4 cups peeled, cored and shredded apple or carrots or zucchini
2 cups white sugar
2 eggs
1 cup chopped walnuts
2 cups all-purpose flour
2 tablespoons ground cinnamon (i like a lot of cinnamon, the original recipe called for 1 tbs)
1 teaspoon ground nutmeg
1 teaspoon salt
2 teaspoons baking soda (make sure it's fresh)
1/2 cup vegetable oil
Preheat oven to 350 degrees. Grease and flour a 9 X 13 inch pan.
In a large bowl, blend the sugar with the eggs. Add the oil, and mix well. Mix in flour, spices, salt, and baking soda. Stir in the nuts and the apples, carrots, or zucchini. Pour batter into prepared pan.
Bake for 40 minutes. Serve warm or cooled.
You could also do this in round pans and make the layer cake like your recipe shows. This is dense -- but it's also somewhat light.. On some occassions, I've done 1/2 apples and 1/2 carrots just to lighten it up a little more.
Good luck .
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