Preheat your oven to 350°F (175°C). Grease and flour an 8-inch (20 cm) square baking pan.
In a medium bowl, whisk together the all-purpose flour, baking soda, baking powder, and salt. Set aside.
In a large bowl, cream the softened unsalted butter and granulated sugar together until light and fluffy, about 3-4 minutes using an electric mixer.
Add the eggs one at a time to the butter and sugar mixture, beating well after each addition.
Mix in the vanilla extract.
In a separate small bowl, combine the mashed bananas, plain yogurt, and whole milk. Stir until smooth.
Add the banana mixture to the wet ingredients and mix until combined.
Gradually add the dry ingredients to the wet ingredients, mixing gently until just combined. Do not overmix.
Pour the batter into the prepared baking pan and spread evenly.
Bake in the preheated oven for 35-40 minutes, or until a toothpick inserted into the center comes out clean.
Remove the cake from the oven and let it cool in the pan for 10 minutes.
Transfer the cake to a wire rack to cool completely before slicing and serving.