For the cookies: Preheat oven to 350 degrees. In a medium mixing bowl stir together flour, baking powder, and salt, set aside.
In a large mixing bowl with an electric mixer on medium speed cream butter and sugar until fluffy. Beat in egg, vanilla, and carrots. On low speed gradually add flour mixture and mix just until blended. Stir in walnuts.
Drop dough by rounded teaspoonfuls onto ungreased baking sheets 1 inch apart. Bake for 15 minutes. Transfer cookies to cooling racks to cool completley.
For the glaze: In a small mixing bowl wisk together powdered sugar, orange juice, and orange zest.
Dip tops of cooled cookies into glaze and place on cooling racks to set.