Preheat oven to 350°F. Mix flour, cinnamon and baking soda in medium bowl. Set aside. Beat butter and sugars in large bowl with electric mixer on medium speed until light and fluffy. Add egg, bananas and vanilla; mix well. Gradually beat in flour mixture on low speed until well mixed. Stir in oats.
Drop by rounded tablespoons onto ungreased baking sheets.
Bake 12 to 15 minutes or until lightly browned. Cool on baking sheets 1 minute. Remove to wire racks; cool completely.