1. Preheat oven to 350 degrees. Position rack to center of oven. Butter or non-stick spray 9” round pan (8”x8” square pan also works). Line the bottom of the pan with parchment paper. 
2. Add sugar, eggs and orange zest to a large bowl and whisk until pale and slightly foamy. Add olive oil, cardamom, cinnamon and salt. Whisk until the mixture is emulsified.
3. In a small bowl, add flour, baking powder and baking soda; stir to combine and set aside.
4. Grate carrots and zucchini. For zucchini, place a clean kitchen towel under the grater.  Wrap zucchini in the towel and squeeze out as much water as possible.
5. Using a rubber spatula, stir in the grated carrots, zucchini and pecans (if using) into egg mixture.
6. Stir in the dry ingredients until just combined. 
7. Pour the batter into the prepared pan. Smooth batter with spatula gently to edges. Gently tap on the counter to release any air bubbles. 
8. Bake the cake until golden in color, approximately 40-50 minutes. Tester in the center of the cake will come out clean. Allow the cake to cool completely before removing from the pan. 
9. Make the frosting. In a mixing bowl fitted with the paddle attachment, cream butter and cream cheese until completely smooth. Slowly add in powdered sugar, followed by orange zest and vanilla. Cream until smooth. Once the cake is completely cool, frost the top of the cake. 

Tips

A 9” spring form pan is my favorite pan for this cake.