Preheat the oven to 350 degrees F (175 degrees C). Grease and flour a 6-inch cake pan.
Sift all-purpose flour, whole wheat flour, baking powder, baking soda, cinnamon, and salt together in a bowl.
Mix honey, oil, and yogurt together in a bowl, stirring gently.
Combine carrots with the honey mixture; add orange zest and vanilla extract. Add flour mixture by the spoonful, folding gently until no dry spots remain. Add a couple teaspoons orange juice if batter is too thick. Pour into the prepared cake pan.
Bake in the preheated oven until the top springs back when touched, 25 to 30 minutes. Allow to cool in the pan for 10 minutes; transfer to a wire rack to cool completely.