Preheat oven to 350 degrees F (175 degrees C). Grease a 6 cup ring mold.
Combine the egg, peanut butter, olive oil, vanilla, and honey in a large bowl; blend well. Stir in the carrots and mix thoroughly. Sift together the flour and baking soda and fold into the carrot mixture. Spoon cake batter into prepared pan.
Bake in preheated oven for 40 minutes. Let cake cool in pan for 10 minutes; then turn out onto a wire rack to cool completely.