Preheat oven to 350 degrees F.
With a mixer, beat butter and sugar until crumbly.
Add carrots, egg, vanilla and orange zest to sugar mixture and beat until well mixed.
Sift flour, salt and baking powder. Then, gradually add to dough, mixing well.
Drop by spoonfuls onto cookie sheet.
Bake 15 minutes until golden.
Make glaze while cookies are cooling by combining hot orange juice and powdered sugar. Stir until all lumps are smooth, then stir in zest.
Drizzle glaze on top of cooled cookies.
Sprinkle with additional orange zest for garnish (if desired).