Simmer carrots on top of the stove until cooked.

Mash well, measure out one cup and set aside.

In a large mixing bowl, cream sugar and butter.

Add egg and the five remaining ingredients. Mix thoroughly.

Drop by teaspoonful on an ungreased cookie sheet.

Bake in a 350-degree F oven for 12-18 minutes or until golden brown.

Combine frosting ingredients adding milk by teaspoonfuls if too stiff.

Ice cookies while still warm. Store in a covered container.