Make the Vanilla Custard:

1. In a medium saucepan, whisk together ⅓ cup sugar and cornstarch until no lumps remain.
2. Beat the egg yolks with the milk in a separate bowl, then pour into the saucepan with the sugar mixture.
3. Cook over medium heat, stirring constantly with a whisk, for 10-12 minutes until the mixture thickens enough to coat the back of a spoon.
4. Remove from heat and stir in 1/12 teaspoon vanilla extract. Let cool for 10 minutes.

Layer the Pudding:

1. In a 1-quart baking dish, arrange about half of the vanilla wafers to cover the bottom.
2. Layer half of the banana slices over the wafers.
3. Pour half of the vanilla custard over the bananas, spreading gently to cover.
4. Repeat with remaining wafers, bananas, and custard.

Make the Meringue:

1. Preheat oven to broil, positioning rack about 6 inches from heating element.
2. In a clean, grease-free bowl, beat egg whites with an electric mixer on high speed until soft peaks form, about 2-3 minutes.
3. Gradually add 2 tablespoons sugar, 1 teaspoon at a time, beating continuously.
4. Add ¼ teaspoon vanilla and continue beating until stiff peaks form and the meringue looks glossy.

Finish and Serve:

1. Spread meringue over the pudding, making sure it touches the edges of the dish all around to seal.
2. Use the back of a spoon to create peaks and swirls in the meringue.
3. Broil for 2-3 minutes, rotating once, until meringue is golden brown. Watch carefully to prevent burning.
4. Let cool for 15 minutes, then refrigerate for at least 2 hours before serving.