Preheat oven to 350°F.
Sift flour, baking powder, baking soda, salt, and spices together in a medium bowl. Set aside.
In a stand mixer, beat eggs, sugar, and vegetable oil together on medium speed. Add sifted dry ingredients in batches and beat until smooth on medium speed. Stir in zucchini, carrots, and vanilla. (This can be done by hand and without a stand mixer; it just might take a bit more elbow grease.)
Lightly grease and flour a bundt pan, and pour in batter. Bake for 45–60 minutes until the top is golden and an inserted toothpick comes out clean. Let cool and sprinkle with powdered sugar.