In a large bowl with electric mixer, beat butter and sugar until light and fluffy. Add egg, grated carrot and vanilla, mixing well. Sift together flour, baking powder and salt and stir into carrot mixture. Stir in chopped nuts, if using. Drop by teaspoonfuls onto greased or parchment lined baking sheets. Bake at 350 degrees for about 14 minutes or until slightly browned on top. When cool, top with cream cheese frosting.
For the Frosting:
Beat together cream cheese and softened butter. Mix in powdered sugar, vanilla, salt and orange flavoring or zest. Note: If you prefer the basic cream cheese frosting, omit the orange flavoring or zest.