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Heat oven to 350 degrees Fahrenheit. Whisk together flour, cocoa, baking powder, baking soda, and salt until well combined.
Stir together carrots, orange zest, honey, applesauce, 1 teaspoon vanilla, and walnuts, if using.
Add wet ingredients to dry ingredients and stir until just combined.
Pour into a buttered 8-inch square baking pan and spread evenly. Bake 25 to 30 minutes, until center is set.
Allow cake to cool in pan 10 minutes, then transfer to a cooling rack to cool completely.
Beat cream cheese and butter together until light and fluffy. Add powdered sugar 1/4 cup at a time; stir in remaining 1 teaspoon vanilla until smooth.
Evenly spread icing over top of cake. Enjoy!