Preheat the oven to 350°F (175°C). Grease and flour an 8-inch round cake pan.
In a large bowl, cream together the softened butter and granulated sugar until light and fluffy.
Add the eggs one at a time, beating well after each addition.
Mix in the vanilla extract and mashed bananas until 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 milk, 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 30 to 35 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.