Pour 1 quart of cold water over the tapioca in a large bow and allow the tapioca to soak for 12 hours. Drain the pearls in a fine mesh strainer.
Combine the milk, vanilla, 1/2 cup sugar, and the salt and in a large saucepan and set aside.
In a heat proof bowl, whisk together the eggs and yolks until well combined. Slowly add the remaining 1/2 cup sugar, whisking constantly, until all of the sugar is incorporated. Whisk until the egg mixture is a very light yellow color, about two minutes, then set aside. Alternately, you can use a hand mixer to do this.
Place the saucepan with the milk mixture over low heat and bring to a simmer. Once it begins to bubble at the edges, remove the pot from heat and drizzle a ladle full of the hot milk into the egg mixture, whisking constantly. Repeat this once again.
Once the milk is mixed evenly into the egg, pour the mixture back into the pot with the milk and and add the tapioca. Whisk constantly over low heat as it starts to thicken. The pearls will become mostly translucent with just a bit of cloudiness in the centers when the pudding is done.
Gently stir in the chopped chocolate until it is all melted incorporated into the pudding making it evenly coloured. The pudding will be somewhat watery, but will thicken up as the tapioca absorbs more of the liquid and cools. Transfer the pudding to a bowl or individual serving dishes, then press plastic wrap directly onto the surface of the pudding. Serve warm or chill in the fridge, at least 2 hours.