Preheat oven to 350 °F. Cream shortening with sugar. Blend in egg.
Stir in carrots. Sift together flour, salt and baking powder; add to creamed mixture.
Add vanilla. Drop by teaspoonfuls on greased baking sheet. Bake for 8 - 10 minutes. Mix ingredients for icing. Ice cookies while warm. Yields 3 dozen cookies.