Adjust oven rack to middle position and preheat to 325ºF (160ºC). Set four 4-ounce ramekins in a large roasting pan; set aside.

Place chocolate in a large mixing bowl; set aside. In a small saucepan, bring milk, heavy cream, and salt to a boil over medium heat. Pour over chocolate and let sit until chocolate begins to melt, about 3 minutes. Whisk until smooth.

In a small bowl, whisk yolks, sugar, and vanilla extract to combine. Add yolk mixture to chocolate mixture and whisk until smooth.

Divide mixture evenly between ramekins. Pour just boiled water (around 180 to 200ºF; 88 to 93ºC) into baking dish until it comes ⅔ of the way up the ramekins; be careful not to splash water into ramekins as you pour.

Carefully transfer roasting pan to middle rack of oven and bake until puddings are just set, about 45 minutes.

Remove roasting pan from oven and carefully remove ramekins from roasting pan; let cool on a wire rack for 15 minutes.

Refrigerate until chilled and set, about 4 hours. Top with whipped cream and chocolate shavings, if desired.