Preheat your oven to 350°F (175°C). Grease a 9x13 inch baking dish with cooking spray or butter.
In a medium bowl, whisk together the instant vanilla pudding mix and milk until smooth and thickened. Stir in the vanilla extract and set aside.
In a separate large mixing bowl, combine the crushed vanilla wafers, self-rising flour, granulated sugar, melted butter, buttermilk, cinnamon, and nutmeg. Mix until just combined; the batter will be slightly lumpy.
Pour the batter into the prepared baking dish, spreading it evenly across the bottom.
Slice the bananas and layer them over the batter, distributing them evenly.
Spoon the prepared vanilla pudding mixture over the banana layer, ensuring it covers the fruit evenly.
Bake in the preheated oven for 35-40 minutes, or until the cobbler is golden brown and a knife comes out clean.
Allow the cobbler to cool slightly before serving.