Preheat oven to 350°. In a large bowl, cream butter, cream cheese and sugars until blended. Beat in eggs, bananas, rum and vanilla. In another bowl, whisk flour, cinnamon, baking powder, salt and baking soda; gradually beat into creamed mixture. Stir in oats and walnuts.
Shape rounded teaspoons of dough into balls; roll in additional brown sugar. Place 1 in. apart on ungreased baking sheets.
Bake until edges begin to brown, 10-12 minutes. Remove from pans to wire racks to cool. Store in airtight containers.