2. In a bowl, pour 1/2 cup of the milk. Add 1/3 cup of the sugar, the eggs, egg yolk, and cornstarch. Whisk until smooth; set aside.
3. In a small, heavy saucepan, combine the remaining 2 cups milk with the remaining 3 tablespoons sugar. Bring almost to a boil over medium heat.
4. Whisking constantly, slowly pour the hot milk into the egg mixture. Return the mixture to the saucepan, and bring to a boil, whisking constantly. Lower the heat and let the mixture bubble gently, still whisking, for 2 minutes or until it is thickened and smooth. Immediately remove the pan from the heat.
5. Strain the hot custard into the bowl. Whisk in the butter and vanilla and stir until the butter melts.
6. Spoon a little custard into the serving bowl. Peel and slice the bananas and scatter a layer of banana slices on top, then finish with a layer of custard. Place a sheet of plastic wrap directly on the surface of the custard. Refrigerate for at least 2 hours or until cold. Adapted from "Classic Home Desserts."