Preheat the oven to 350°F (175°C).

In a large mixing bowl, whisk together the eggs, brown sugar, vegetable oil, honey, and vanilla extract for about 2 minutes until well combined.

Gently fold in the grated carrots and zucchini into the wet mixture, adding walnuts if using.

In a separate bowl, combine flour, baking powder, ground ginger, and baking soda, stirring until even.

Gradually add the dry mixture into the wet bowl, stirring gently until just mixed.

Pour the thick batter into an ungreased 13x9x2-inch baking pan and spread it evenly.

Bake for approximately 25 minutes or until a toothpick inserted comes out clean.

Cool the bars on a wire rack for about 1 hour.

Prepare the frosting by beating cream cheese, powdered sugar, lemon zest, and juice until smooth.

Once cooled, frost the bars generously and cut into squares before serving.