PREHEAT oven to 350º F.
COMBINE butter, brown sugar and sugar in large mixer bowl. Beat at medium speed, scraping bowl often, until creamy. Add pumpkin, egg and vanilla extract. Continue beating for 1 to 2 minutes or until well mixed. Reduce speed to low; beat in flour, 1 1/2 teaspoons pumpkin pie spice, baking powder, baking soda and salt. Stir in 1 cup walnuts by hand. Drop by rounded teaspoonfuls 2 inches apart onto ungreased cookie sheets.
BAKE for 8 to 10 minutes or until set. Cool on baking sheets for 2 minutes; remove to wire racks to cool completely.
COMBINE powdered sugar, butter, cream cheese, vanilla extract and pumpkin pie spice in medium mixer bowl. Beat at low speed, scraping bowl often, until smooth. Frost cooled cookies. Garnish with walnuts.