Preheat the oven to 350°F. Line two large rimmed baking sheets with parchment paper; set aside. Toast cardamom and cinnamon in a small skillet over medium, shaking skillet often, until fragrant, about 2 minutes. Remove from heat. Whisk together cardamom mixture, flour, salt, and baking soda in a medium bowl; set aside.

Beat brown sugar, butter, and granulated sugar in a stand mixer fitted with the paddle attachment on medium-high speed until creamy, about 1 minute. Reduce mixer speed to low, and gradually add flour mixture to butter mixture, beating until combined, about 1 minute. Add banana, egg, and vanilla; beat until combined, about 30 seconds. Stir in oats and chocolate chips.

Drop 24 portions of dough (1 1/2 tablespoonfuls each), spaced 2 inches apart, on prepared baking sheets. Bake in a preheated oven, one sheet at a time and rotating the baking sheet halfway through bake time, until cookie edges are golden brown and set, 10 to 12 minutes per batch. Let cookies cool to room temperature on a baking sheet, 10 to 15 minutes.