Prepare Banana Filling. Refrigerate for 20 minutes.
Preheat oven to 350 F. In a large bowl, cream together butter and sugars until pale and fluffy. Beat in egg and vanilla. Stir in peanut butter.
In a separate bowl, combine flour, baking soda, and salt. Add to peanut butter mixture and blend in.
Drop by tablespoonfuls onto an ungreased cookie sheet and crisscross mark them with a floured fork. Bake approximately 9 to 11 minutes or until cookies just start to turn brown around the edges. Remove from heat and let cool on a wire cooling rack.
When cookies are cool, spread Banana Filling between 2 peanut butter cookies to make sandwiches. Repeat with remaining cookies.
In a frying pan over medium heat, melt butter. Add sugars and increase heat to medium-high, stirring until melted and bubbling. Carefully add rum (watch out for flames). Add cinnamon. Stir in bananas to coat, set aside.
Cream together cream cheese and peanut butter until smooth. With a fork. mash bananas and add to cream cheese mixture until smooth. Refrigerate for 20 minutes before spreading on the cookies.
Sweet Banana Peanut Butter Cookies Recipe: https://whatscookingamerica.net/cookie/bananapeanutbuttercookie.htm