Set the oven at 350° F. Have on hand a 2-quart high-sided casserole or soufflé
dish.
Layer the cookies in the dish and cover them with the banana slices.
In a large heavy saucepan, combine 3/4 cup of sugar and the flour. Stir in the
milk. Cook over medium heat, stirring constantly, until the mixture thickens.
Cook, stirring, 2 minutes more. Remove the pan from the heat.
In a medium bowl, whisk the egg yolks. Slowly whisk in about 1 cup of the
thickened milk mixture. Then, gradually whisk the egg mixture back into the milk
mixture in the saucepan. Bring to a gentle boil. Lower the heat and cook,
stirring, for 2 minutes more.
Remove the pan from the heat and stir in the butter and 1 1/2 teaspoons of the
vanilla. Pour the pudding over the bananas.
In an electric mixer, beat the egg whites until foamy. Add the remaining 1
teaspoon of vanilla and 2 tablespoons sugar. Continue beating until the whites
hold stiff peaks.
Spread the meringue in a thick layer over the pudding, making sure it reaches
the edges. Decorate the top with little peaks, if you like.
Bake the pudding for 10 to 15 minutes or until the meringue is golden brown.
Cool on a rack and serve at room temperature (it will be quite loose) or
chilled.
