Preheat the oven to 350°F (175°C). Grease and flour an 8-inch round cake pan.
In a large bowl, cream the softened unsalted butter and granulated sugar together until light and fluffy using a hand mixer or stand mixer.
Add the eggs one at a time, beating well after each addition.
Mix in the vanilla extract and mashed ripe bananas until fully combined.
In a separate bowl, whisk together the all-purpose flour, baking soda, baking powder, and salt.
Gradually add the dry ingredients to the banana mixture alternately with the buttermilk, beginning and ending with the dry ingredients. Mix gently until just combined without overmixing.
Pour the batter into the prepared cake pan and smooth the top with a spatula.
Bake for 35 to 40 minutes, or until a toothpick inserted into the center comes out clean.
Remove the cake from the oven and allow it to cool in the pan for 10 minutes.
Transfer the cake to a wire rack to cool completely before serving.