01 - Preheat oven to 350°F. Line a 9×13-inch baking pan with parchment paper, leaving an overhang on the sides for easy removal.
02 - In a medium bowl, whisk together the all-purpose flour, whole wheat flour, baking powder, baking soda, salt, ground ginger, cinnamon, nutmeg, and cloves until evenly distributed.
03 - In a large bowl, beat the brown sugar, vegetable oil, eggs, vanilla extract, and applesauce until smooth and well combined.
04 - Gently fold the grated carrots, grated zucchini, and crystallized ginger (if using) into the wet mixture.
05 - Add the dry ingredient mixture to the wet ingredients and stir until just combined. Be careful not to overmix.
06 - Spread the batter evenly into the prepared baking pan. Bake for 30 to 35 minutes, or until a toothpick inserted in the center comes out clean.
07 - Allow the bars to cool completely in the pan on a wire rack before frosting.
08 - Beat the softened cream cheese and butter together until smooth. Mix in the sifted powdered sugar, fresh lemon juice, lemon zest, and vanilla extract until light and fluffy.
09 - Once the bars are fully cooled, spread the lemon cream cheese frosting evenly over the top. Cut into 12 bars and serve.