Overripe bananas are naturally sweet, so you can use less sugar to make this cake.

Preheat oven to 350°F. Coat an 8-inch-square baking pan with cooking spray and line the bottom with parchment paper.

Whisk whole-wheat flour, all-purpose flour, baking powder, cinnamon, baking soda, cardamom and salt in a medium bowl. Whisk banana, buttermilk (or yogurt) and vanilla in a small bowl.

Beat brown sugar, butter and oil with an electric mixer in a large bowl until light and fluffy, about 2 minutes. Scrape down the sides and add eggs, one at a time, beating well after each addition. Fold in the flour and banana mixtures in 2 alternating additions, starting and ending with the flour. Gently stir in chocolate. Scrape the batter into the prepared pan.

Bake the cake until a toothpick inserted in the center comes out clean, 25 to 30 minutes. Let cool to room temperature in the pan on a wire rack, about 30 minutes. Invert the cake onto a plate and remove the parchment paper.

Store airtight at room temperature for up to 3 days.