Preheat oven to 400 degrees F (200 degrees C).

Combine butter and brown sugar in a large bowl; mix together with an electric mixer until light and fluffy. Beat in carrots and egg.

Combine all-purpose flour, whole wheat flour, cinnamon, baking powder, nutmeg and salt in a bowl. Stir into carrot mixture, a little at a time, blending dough well after each addition.

Drop spoonfuls of dough 2 inches apart onto a baking sheet; flatten with a moistened fork.

Bake in the preheated oven until cookies are golden and crisp, about 15 minutes. Transfer to wire racks to cool, about 15 minutes.