Preheat oven to 375 degrees F (190 degrees C). Line a baking sheet with parchment paper.
Beat butter and brown sugar together in a bowl using an electric mixer until smooth and creamy; add egg and vanilla extract and beat until incorporated.
Whisk all-purpose flour, whole wheat flour, baking powder, cinnamon, baking soda, and cloves together in a bowl; stir into butter mixture until just incorporated. Fold oats, carrots, raisins, and walnuts into dough. Drop large mounds of dough onto the prepared baking sheet and sprinkle each with coarse sugar.
Bake in the preheated oven until edges are lightly browned, 10 to 12 minutes.