Preheat the oven to 350°F (175°C). Grease and flour an 8-inch round cake pan.
In a medium bowl, whisk together the flour, baking soda, and salt. Set aside.
In a large bowl, cream the softened butter and granulated sugar together until light and fluffy, about 3-4 minutes.
Add the eggs one at a time, beating well after each addition. Stir in the vanilla extract.
Mix in the mashed bananas.
Alternately add the flour mixture and buttermilk to the banana mixture, beginning and ending with the flour mixture. Stir until just combined.
Pour the batter into the prepared cake pan and smooth the top with a spatula.
Bake for 40-45 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 and cool completely before serving.