In a small saucepan or in the microwave, warm up the milk without bringing it to a boil.
1 cup Whole Milk
In a separate saucepan, melt the butter over medium-low heat. Add the sugar and whisk until fully dissolved.
3 tablespoon Butter, ¼ cup Sugar
Add the roughly chopped chocolate, and when it's fully melted sift in the cornstarch or flour, whisking constantly.
2.6 oz Dark Chocolate, 2 tablespoon Cornstarch
Pour the hot milk in, while keeping on stirring, then add the vanilla and cook for a few minutes until it starts to thicken.
1 pinch Vanilla
When it's pudding consistency, immediately pour into the molds and tap them to remove air bubbles. Let them cool down at room temperature, then move to the fridge to set for a couple of hours.
To unmold the fully set budino, dip the silicon side of the molds into hot water for a few seconds, then flip onto a plate and pat vigorously until the budino flops down on the plate.
Notes
Use high-quality dark chocolate for the richest flavor.
For a silkier texture, you can strain the pudding before pouring into cups.
Stir constantly when cooking to prevent the budino from sticking or forming lumps.