Prepare the custard base: In a medium bowl, whisk together the sweetened condensed milk, evaporated milk, and cold water.
Add the instant vanilla pudding mix and vanilla extract to the milk mixture. Whisk for two minutes until slightly thickened. Set aside.
Make the meringue: In a separate, clean bowl, beat the egg whites until soft peaks form. Gradually add the granulated sugar and cream of tartar, beating until stiff, glossy peaks form.
Gently fold one-third of the meringue into the pudding mixture to lighten it. Then, fold in the remaining meringue until just combined. Do not overmix.
Assemble the pudding: In a large glass serving dish, create a layer of vanilla wafers. Top the wafers with a layer of sliced bananas.
Spoon half of the pudding mixture evenly over the bananas and wafers. Repeat the layers: wafers, bananas, and the remaining pudding.
Spread the meringue evenly over the top layer of pudding, making sure to seal the edges to the dish.
Bake: Place the dish in a preheated oven at 350°F (175°C) for about 15 minutes, or until the meringue is lightly golden brown.
Cool completely before serving. Chill for at least 4 hours for the best texture.
Notes
For a no-bake version, skip the meringue and egg whites. Instead, top the final pudding layer with crushed vanilla wafers or whipped cream.
Slice bananas just before assembling to prevent browning.