Preheat the oven to 350°F (175°C). Grease and flour a 9×5 inch loaf pan.
In a medium bowl, whisk together the all-purpose flour, baking powder, baking soda, and salt. Set aside.
In a large bowl, cream the softened unsalted butter and granulated sugar together until light and fluffy using an electric mixer or by hand.
Add the eggs one at a time to the butter and sugar mixture, beating well after each addition.
Mix in the pure vanilla extract.
Stir in the mashed ripe bananas until evenly combined.
Add the dry ingredients to the wet ingredients in three additions, 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 allow it to cool in the pan for 10 minutes.
Transfer the banana cake loaf to a wire rack and cool completely before slicing.