Preheat the oven to 350°F (175°C). Grease and flour a 9x5-inch loaf pan.
In a medium bowl, whisk together the flour, baking powder, baking soda, and salt. Set aside.
In a large mixing bowl, cream the softened butter and granulated sugar together until light and fluffy, about 3-4 minutes.
Add the eggs one at a time, mixing well after each addition. Stir in the vanilla extract and mashed bananas until combined.
Gradually add the dry ingredients to the wet mixture, alternating with the sour cream, starting and ending with the flour mixture. Mix until just combined.
Fold in the crushed vanilla wafers and banana pudding until evenly distributed.
Pour the batter into the prepared loaf pan and smooth the top. Sprinkle additional crushed vanilla wafers on top for added crunch.
Bake for 60-70 minutes, or until a toothpick inserted into the center comes out clean. Allow the cake to cool in the pan for 10 minutes before transferring it to a wire rack to cool completely.
Slice and serve the cake at room temperature.