In a bowl, whisk together the all-purpose flour, whole wheat flour, baking powder, baking soda, cinnamon, and salt.
In another large bowl, cream together the softened butter, brown sugar, and granulated sugar until light and fluffy.
Add the egg and vanilla extract to the butter-sugar mixture. Mix until well combined.
Gradually add the dry ingredients to the wet ingredients, mixing until just combined.
Fold in the grated carrots and chopped nuts (if using).
Drop rounded tablespoons of batter onto the prepared baking sheets, leaving space between each cookie.
Bake for 10-12 minutes or until the edges are golden. Allow the cookies to cool completely.