Preheat oven to 350°F (175°C) and line two baking sheets with parchment.
Beat butter and brown sugar until creamy, then add egg, mashed bananas, molasses, and vanilla; mix until combined.
Whisk flour, baking soda, salt, and spices in a bowl; stir into wet mixture until just combined. Fold in oats if using.
Drop tablespoons of dough onto prepared sheets, leaving 2 inches between. Sprinkle with coarse sugar if desired.
Bake 10–12 minutes until edges set but centers are still soft. Cool on pans 5 minutes, then transfer to a rack.