For cookies, preheat oven to 350° F. 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 for 9 to 11 minutes, until cookies just start to colour around the edges.
For filling, in sauté pan, melt butter over medium heat. Add sugars and increase heat to medium-high. Stir until melted and bubbling. Add rum (watch out for flames). Add cinnamon. Stir in bananas to coat, set aside.
Cream together cream cheese and peanut butter until smooth. Mash bananas and add to cream cheese mixture until smooth. Chill for 20 minutes.
Fill between 2 peanut butter cookies to make sandwiches. Repeat with remaining cookies.