Gather your ingredients and grab a medium saucepan. Combine the milk, cream, sugar, and butter. Turn your stovetop heat to medium.
As the mixture heats, keep an eye on it and stir occasionally. We want the butter and sugar to melt completely, and the mixture to start steaming – a sign it's getting happy and ready for the next step.
While the milk mixture works its magic, let's create our thickening agent. In a separate bowl, whisk together the cornstarch with ¼ cup of water. If you're feeling adventurous, swap the water for bourbon or rum for a boozy twist!
Once the milk mixture is steaming, slowly whisk in the cornstarch mixture. Here comes the important part: keep stirring constantly! This ensures the sauce thickens evenly and smoothly. You'll know it's ready when the sauce reaches a nice, nappe consistency – that means when you spoon some sauce, it coats the back of the spoon without being runny.
Remove the pan from the heat and stir in the vanilla extract. If you choose to add a touch of rum, now's the time!
Pour some of this delightful sauce over your warm bread pudding, and don't forget to serve the rest on the side for extra drizzling fun!