Preheat oven to 350 degrees Fahrenheit (175 degrees Celsius) and grease a 9x13 inch baking pan.

Whisk together flour, baking soda, salt, and ground cinnamon in a medium mixing bowl.

Cream the softened butter and brown sugar in a large bowl until the mixture is light and fluffy.

Incorporate the beaten eggs, mashed bananas, buttermilk, and vanilla extract into the butter mixture, blending thoroughly.

Gradually fold the dry flour mixture into the wet ingredients until just combined, ensuring not to overmix.

Transfer the batter into the prepared baking pan and smooth the surface with a spatula.

Bake for 45 to 50 minutes or until a toothpick inserted into the center of the cake comes out clean.

Remove from the oven and allow the cake to cool completely in the pan on a wire rack before serving.