Preheat oven to 325. Grease a 9 x 5-inch loaf pan.
Sift together flour, baking soda, baking powder, salt, and spices. With the mixer on low speed, add in flour until batter forms. Pour in a loaf pan.
In a stand mixer on medium speed, combine eggs and sugar. Add butter and vanilla until well combined, approximately 5 minutes. Gently fold in zucchini and carrot.
With the mixer on low, add flour mixture. Stir until well combined. Spoon batter into a loaf pan.
Bake for 1 hour. Let bread cool in a pan for 10 minutes. Remove from pan and finish cooling on a baking rack.