Preheat oven to 350 degrees F. In a large bowl, whisk together the eggs, brown sugar, oil, honey, and vanilla. Don’t worry about clumps of the brown sugar, those will dissolve as it sits while you prepare the remaining ingredients. Then fold in the carrot, zucchini, and walnuts.
In another bowl combine add the flour, baking powder, ginger, and baking soda. Whisk to blend together.
Add to flour mixture to the wet mixture. Stir just until combined. Spread batter into a greased 13x9 inch baking pan.
Bake about 25 minutes or until a toothpick inserted in center comes out clean. Cool completely in pan on a wire rack.
Once the cake is cooled prepare the frosting. In a medium mixing bowl, beat the fosting ingredients with an electric mixer on medium speed until fluffy. Spread or pipe the frosting over the cooled bars.