Preheat the oven to 350°F (175°C). Grease and flour a 9×9-inch square baking pan.
In a medium bowl, whisk together the flour, baking powder, baking soda, and salt. Set aside.
In a large bowl, using an electric mixer, beat the softened butter and granulated sugar until light and fluffy, about 3 minutes.
Add the eggs one at a time, beating well after each addition. Mix in 1 teaspoon vanilla extract.
Add the mashed bananas to the butter mixture and mix until combined.
Alternately add the dry ingredients and buttermilk to the banana mixture, beginning and ending with the dry ingredients. Mix until just combined.
Pour the batter into the prepared baking pan and spread evenly.
Bake for 30-35 minutes or until a toothpick inserted into the center comes out clean.
Remove the cake from the oven and let it cool completely in the pan on a wire rack.
While the cake is cooling, prepare the vanilla pudding by whisking the instant vanilla pudding mix with 2 cups cold whole milk in a medium bowl. Let it set for 5 minutes until thickened.
In a large bowl, beat the heavy whipping cream, powdered sugar, and 1 teaspoon vanilla extract with an electric mixer until stiff peaks form. Set aside.
Once the cake is completely cooled, cut it into 1-inch cubes.
In a large trifle bowl or individual serving glasses, layer one-third of the banana cake cubes.
Top with one-third of the vanilla pudding, then a layer of sliced bananas, and then one-third of the whipped cream.
Repeat the layers two more times, finishing with whipped cream on top.
Refrigerate the assembled trifle for at least 2 hours before serving to allow flavors to meld.
Serve chilled and enjoy your Banana Cake Trifle!