Preheat your oven to 350°F and prepare an 8×8-inch baking dish by lining it with parchment paper or coating it with nonstick spray. In a medium bowl, whisk together the flour, cinnamon, baking soda, baking powder, salt, nutmeg, and ginger until evenly mixed. In another bowl, cream the softened butter with both sugars using medium speed until the texture becomes light and fluffy. Beat in the eggs and vanilla extract just until incorporated. Blend in half of the dry mixture, then add the remaining half and continue mixing until no streaks of flour remain—avoid overmixing. Fold in the shredded carrots gently. Transfer the batter into the prepared pan, smoothing the top. Bake for 35 to 40 minutes, or until a toothpick inserted in the center comes out clean. Let cool in the pan for 5 to 10 minutes, then move to a wire rack to cool completely before frosting.

To prepare the frosting, combine the softened cream cheese, butter, and vanilla in a medium bowl and beat on medium speed until creamy. Gradually incorporate the powdered sugar, one cup at a time, mixing well between additions until a smooth consistency is achieved. For decorative frosting, divide about ½ cup of the finished frosting into two bowls and tint one with orange and the other with green food coloring. Stir each until fully colored, then transfer to piping bags or zip-top bags with corners trimmed.

Evenly spread the remaining frosting over the cooled cake surface. Slice into 16 bars. Use the colored frosting to pipe carrot designs onto each piece, creating a whimsical presentation.