Preheat oven to 350 degrees. Line two large baking sheets with parchment paper.
In the bowl of an electric mixer, beat together the butter and sugars until well combined. Add the egg, vanilla extract and mashed bananas and beat on medium speed until combined, scraping down the bowl as needed.
In another bowl, whisk together the flour, cinnamon, baking soda, salt and cornstarch. Add it to the mixer and beat on low speed until combined. Stir in oats.
Spoon tablespoons of dough onto prepared cookie sheets. Flatten dough a bit with the palm of your hand, into thick discs. They will spread a little when baked. Bake for 10-12 minutes or until edges are golden and top is no longer sticky.
Remove from oven and cool on cookie sheet for 3-4 minutes, then use a spatula to move them to a cooling rack to finish cooling.