The banana pudding recipe from Spicy Southern Kitchen is a good homemade version of the dish. It consists of homemade pudding layered with fresh banana slices and vanilla wafers, topped with whipped cream.
To make banana pudding, whisk together 4 egg yolks, 1/4 cup of sugar and 3 tablespoons of cornstarch in a bowl. Pour 2 cups of half and half, 1 cup of whole milk, 1/2 cups of sugar and 1/4 teaspoon of salt into a heavy saucepan. Bring the mixture to a simmer over medium heat to dissolve the sugar, stirring constantly. Add the mixture in the pan to the egg yolk mixture very gradually, whisking constantly.
Return the mixture to the pan and stir it over medium heat until thickened, or approximately 2 to 3 minutes. Remove the pan from the heat. Cut 2 tablespoons of butter into 4 pieces, and stir it into the pan along with 1 teaspoon of vanilla extract. Place a thin layer of this pudding mixture into the bottom of a casserole dish. Cover this bottom layer with a layer of vanilla cookies and then a layer of sliced bananas. Repeat these layers until the pudding is used up. For the topping, beat some whipping cream in a bowl until peaks form, and spread the whipped cream over the top of the pudding.