Preheat oven to 350 degrees F. Coat an 9- x 5-inch loaf pan with non-stick cooking spray.
In medium bowl stir together flour, baking powder, baking soda, salt, cinnamon, ginger, and nutmeg. Set aside.
Add eggs and brown sugar to a large mixing bowl and beat with an electric mixer until smooth. Add oil, pure maple syrup, and vanilla, and mix again until well blended. Add about half of the flour mixture and mix just until incorporated. Add remaining flour mixture and continue to mix until combined. Using a wooden spoon, stir carrot and zucchini into the batter.
Pour batter into the prepared loaf pan. Bake 45 to 50 minutes, or until toothpick inserted in center comes out clean. Let cool for 15 to 20 minutes before removing from pan. Allow to cool completely before frosting.
Meanwhile, prepare the frosting.
Use an electric mixer to beat cream cheese together with butter in a medium bowl. Add powdered sugar and mix again until incorporated. Add milk, lemon juice, and vanilla extract and beat until creamy.
Frost the cooled loaf of bread and immediately sprinkle with chopped walnuts, if desired.