Preheat your oven to 350°F (175°C) and prepare a 13x9-inch baking pan by greasing or lining it.

In a large mixing bowl, combine the eggs, brown sugar, vegetable oil, honey, and vanilla extract. Whisk until smooth, about 2-3 minutes.

Fold in the grated carrots, zucchini, and chopped walnuts into the wet mixture.

In a separate bowl, whisk together the all-purpose flour, baking powder, ground ginger, and baking soda.

Gradually mix the dry ingredients into the wet mixture, stirring gently until just combined.

Spread the batter evenly into the prepared baking pan.

Bake in the preheated oven for approximately 25 minutes until a toothpick inserted comes out clean.

Let the bars cool completely in the pan on a wire rack for about 30-45 minutes.

Beat together the cream cheese and lemon zest until fluffy, about 2-3 minutes on medium speed.

Spread the frosting evenly over the cooled bars.