Preheat your oven to 180°C (350°F).
Grease an 8-inch cake pan with butter and dust it lightly with flour.
Strain and combine the flour, ground cinnamon, baking soda, and baking powder in a medium-sized bowl.
Using a larger mixing bowl, mix eggs with brown sugar.
Add honey, olive oil, and one teaspoon of vanilla extract, then continue mixing.
Add the strained, dry ingredients from earlier and mix.
Add the grated carrots and continue mixing to combine everything evenly.
Pour your carrot cake with olive oil batter into the greased cake pan.
Place the pan in the lower part of the oven for 40 to 45 minutes or until a toothpick comes out clean when inserted.
Take your carrot cake out of the oven and set it aside to cool.
Prepare the icing by combining the cream cheese, powdered sugar, and the remaining vanilla extract.
Spread the cream cheese icing on top of the cooled carrot cake.
Use an angled spatula to smoothen the top.
Sprinkle the crushed walnuts over the icing.
Slice and serve your olive oil carrot cake --- sprinkle more walnuts, if preferred!