Bring the milk to a boil with the split and scraped vanilla bean, then add the butter to melt it. Meanwhile, mix the flour and sugar in a mixing bowl. Stir in the eggs, then gradually pour in the hot milk while whisking to create a smooth, runny batter, similar to pancake batter.
Let the mixture cool, then add the rum. Next, place the dough in the refrigerator and let it rest for at least 1 hour to allow the flavors to develop.
Preheat the oven to 240°C (thermostat 8) with the baking sheet inside. If using a silicone mold, limit the temperature to 220°C. Carefully butter the molds, fill them halfway with the well-chilled batter, and then place the molds on the hot baking sheet.
Bake the cannelés for 12 minutes at 240°C (or 20 minutes at 220°C using a silicone mold), then lower the temperature to 180°C and continue baking for about 1 hour. This will result in a nicely caramelized crust and a tender, moist center.
