Preheat oven to 350°F (175°C) and line a baking sheet with parchment paper.
In a bowl, whisk together flour, baking powder, baking soda, cinnamon, nutmeg, and salt.
In a separate bowl, cream butter and brown sugar until light and fluffy.
Beat in the egg and vanilla until fully combined.
Gradually mix in the dry ingredients until just combined.
Fold in the grated carrots gently.
Scoop dough onto the prepared baking sheet, spacing cookies apart.
Bake for 10–12 minutes, until cookies are set and lightly golden.
Cool on the baking sheet for 5 minutes, then transfer to a wire rack.