Preheat the oven to 350°F (175°C) and line a baking sheet with parchment paper.
In a bowl, whisk together the flour, baking powder, and salt.
In a separate large bowl, beat softened butter and sugar until light and fluffy.
Add the egg and vanilla extract to the butter mixture and mix until fully combined.
Gradually add the dry ingredients to the wet ingredients, mixing until a dough forms.
Divide the dough into two portions. Add orange food coloring to one and green food coloring to the other.
Roll out the orange dough to about ¼-inch thickness and cut out carrot shapes using a cookie cutter.
Use the green dough to cut out small leaf shapes or reserve it for piping green icing leaves later.
Place the cut-out cookies on the prepared baking sheet and bake for 8-10 minutes or until the edges are lightly golden.
Let the cookies cool completely before decorating with royal icing.
Pipe green leaves onto the top of each carrot cookie for a festive touch.
Let the icing set before serving or packaging for gifts.