In a large bowl, cream butter, brown sugar, and vanilla. Add egg and mix well.
Add flour, cinnamon, nutmeg, cloves, baking soda, salt and mix until completely combined. Fold in carrots (and raisins and walnuts if you are using them).
Place spoonfuls of dough on ungreased cookie sheets and bake for 9-12 minutes. Remove from cookie sheet and let cool.
Frosting
After the cookies have cooled, prepare cream cheese frosting.
Cream butter, cream cheese, and vanilla together, then add powdered sugar. Add more or less powdered sugar, depending on how thick you want the frosting to be.
Frost cooled cookies and top with additional walnuts if desired.