Heat oven to 350ºF. In large bowl, beat brown sugar and spread with electric mixer until creamy. Add egg and vanilla; beat well. Add bananas; beat well. Add combined flours, pumpkin pie spice, baking soda and salt; mix until blended. Add oats and, if desired, banana chips; mix until blended.
Drop dough by heaping measuring tablespoonfuls 2 inches apart onto ungreased cookie sheets. With narrow metal spatula, spread into 2-1/2 inch circles.
Bake 10 to 12 minutes or until edges are lightly browned. Remove to wire rack. Cool completely. Store tightly covered.
To assemble, spread 2 teaspoons peanut butter on flat side of one cookie. Press second cookie over peanut butter.