Preheat the oven to 350°F (175°C). Grease and flour an 8-inch (20 cm) round cake pan.
In a medium bowl, whisk together the all-purpose flour, baking powder, baking soda, and salt. Set aside.
In a large bowl, beat the softened butter and granulated sugar together with an electric mixer on medium speed until light and fluffy, about 3-4 minutes.
Add the eggs one at a time, beating well after each addition. Mix in the vanilla extract.
Add the mashed bananas to the wet mixture and mix until combined.
Alternately add the dry ingredients and buttermilk to the wet mixture, beginning and ending with the dry ingredients. Mix on low speed until just combined. Do not overmix.
Pour the batter evenly into the prepared cake pan and smooth the top with a spatula.
Bake in the preheated oven for 38-42 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.
Turn the cake out onto a wire rack and let it cool completely before serving.