Heat the Milk: Combine milk, chopped bananas, and vanilla bean (if using) in a medium saucepan. Heat over medium until it almost boils. If not using vanilla bean, just add more vanilla extract at the end.
Infuse: When the milk shows the first bubbles, remove it from the heat. Cover and let the bananas infuse for at least 4 hours or refrigerate overnight.
Reheat: Once infused, reheat the milk over medium until hot.
Mix Yolks and Sugar: In a bowl, whisk egg yolks, granulated sugar, cornstarch, and salt.
Strain Milk: Pour the hot milk through a fine strainer into another bowl, pressing the bananas to get all the milk out. Discard the solids.
Temper the Yolks: Slowly whisk 2 tablespoons of the hot milk into the egg mixture. Gradually add the rest of the milk, whisking constantly.
Cook Custard: Pour the custard back into the saucepan through a fine strainer. Cook over medium, stirring continuously until thick and smooth, about 5-7 minutes.
Add Butter and Vanilla: Remove from heat. Stir in butter and vanilla extract (if using). Pour into a bowl, cover with plastic wrap touching the surface, and chill in the fridge.