Heat oven to 350°F.
Combine flour, baking soda, pumpkin pie spice, baking powder and salt in bowl. Set aside.
Combine brown sugar and 1/2 cup butter in bowl; beat at medium speed until creamy. Add pumpkin, milk, egg and vanilla; beat until well mixed. Add flour mixture; beat at low speed until well mixed.
Drop batter by level measuring tablespoonfuls onto ungreased cookie sheets. Bake 9-10 minutes or until set and lightly browned around edges. Cool 2 minutes on cookie sheets; remove to cooling rack. Cool completely.
Combine all filling ingredients except powdered sugar in bowl. Beat at medium speed, scraping bowl often, until smooth. Gradually add 4 cups powdered sugar, beating well after each addition until creamy.
Spread 2 teaspoons filling onto bottom-side of 1 cookie. Top with another cookie, bottom-side down. Repeat with remaining cookies and filling. Sprinkle filled cookies with powdered sugar.
*Substitute 1/2 teaspoon ground cinnamon plus 1/4 teaspoon ground ginger, 1/4 teaspoon ground nutmeg and 1/8 teaspoon ground cloves.
**Substitute 1/2 cup canned pumpkin.