Preheat the oven to 350°F (175°C). Grease and flour a 9×5-inch loaf pan.
In a large mixing 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.
Stir in the vanilla extract and mashed bananas until combined.
In a separate bowl, whisk together the all-purpose flour, baking powder, baking soda, and salt.
Gradually add the dry ingredients to the banana mixture, alternating with the whole milk, beginning and ending with the dry ingredients. Mix until just combined; do not overmix.
Pour the batter into the prepared loaf pan and smooth the top with a spatula.
Bake in the preheated oven for 50 minutes, or until a toothpick inserted into the center comes out clean.
Remove the loaf from the oven and let it cool in the pan for 10 minutes.
Transfer the loaf to a wire rack to cool completely before slicing.