Preheat your oven to 350°F (175°C) while you prepare the batter.
In a large bowl, combine the lightly beaten eggs, brown sugar, canola oil, honey, and vanilla extract. Whisk until smooth.
Fold in the grated carrots and zucchini along with the chopped walnuts.
In another bowl, whisk together the flour, baking powder, ground ginger, and baking soda. Gradually add to wet ingredients until just combined.
Pour the batter into a greased baking dish and bake for about 25 minutes or until a toothpick comes out clean.
In a mixing bowl, beat together the reduced-fat cream cheese, icing sugar, and lemon zest until smooth.
Once the bars have cooled, spread an even layer of frosting over top and cut into squares or rectangles.