Preheat the oven to 350°F (175°C). Grease and flour an 8-inch round cake pan.
In a medium bowl, whisk together the all-purpose flour, baking soda, and salt. Set aside.
In a large bowl, cream the softened butter and granulated sugar together until light and fluffy using an electric mixer.
Add the eggs one at a time, beating well after each addition.
Mix in the vanilla extract.
Add the mashed bananas and mix until combined.
Alternately add the dry ingredients and buttermilk to the banana mixture, beginning and ending with the dry ingredients. Mix until just combined.
Pour the batter into the prepared cake pan and smooth the top with a spatula.
Bake in the preheated oven for 40 to 45 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 to cool completely before serving.