Makes about 4 dozen 1½ -inch sandwich cookies.
Preheat oven to 400ºF. In large bowl, beat butter and sugar with electric mixer until light and fluffy. Beat in egg and extract. Combine flour, baking powder, pumpkin pie spice and salt; add to butter mixture 1 cup at a time, mixing after each addition. Do not chill dough. Divide dough into 2 balls.
On a floured surface, roll each ball into a circle approximately 12 inches in diameter and 1/8 in. thick. Dip apple cookie cutter in flour before each use. Bake cookies on ungreased cookie sheet 7-8 minutes or until cookies are lightly browned.
Spread apple butter, if desired, then buttercream icing on half of the cookies; cover with remaining cookies.