Preheat the oven to 350°F (175°C) and line two baking sheets with parchment. In a large bowl, cream together the softened butter, brown sugar, and granulated sugar until light and fluffy, about 2 minutes.

In a small bowl, mash the bananas until smooth. Add the mashed banana, egg, and vanilla extract to the butter mixture. Mix until just combined, even if the batter looks slightly curdled.

In a separate bowl, whisk together the flour, baking soda, cinnamon, and salt. Fold the dry ingredients into the wet ingredients just until no streaks of flour remain. If using chocolate chips, fold them in now.

Drop rounded tablespoonfuls (about 1 1/2 tablespoons each) of dough onto the prepared baking sheets, spacing them 2 inches apart. Bake for 10 to 12 minutes, until the edges are set and the tops look dry. Let the cookies cool on the sheet for 5 minutes, then transfer them to a wire rack.