1. Make crumb mixture: Mix together bread crumbs, sugar, cinnamon and butter.
2. Make filling: Position a rack in lower third of oven and preheat to 350ºF. In a heavy pan, bring milk to a simmer. With an electric mixer, beat eggs, sugar, cornstarch, flour and salt until thick and pale yellow. Gradually pour half of milk into egg mixture, whisking constantly, then whisk this mixture gradually into milk in pan. Cook over low heat, whisking constantly, until mixture has thickened, 1 minute (do not overcook). Remove from heat and stir for 1 minute. Add vanilla and rum, if desired. Fold bananas into hot custard.
3. Gently press half of crumb mixture into bottom of a 9-inch baking dish. Top with banana mixture, then remaining crumbs. Bake until top has browned and starts to bubble, 25 to 30 minutes.