Preheat the oven to 325 degrees F. Heat the heavy cream, milk, vanilla and salt in a small saucepan over medium heat until just starting to bubble. Remove from the heat and cover to keep warm.
Make the caramel: Combine the sugar and 1/4 cup water in another small saucepan over medium heat, stirring just until the sugar dissolves. Cook, swirling the pan occasionally but not stirring, until amber, about 10 minutes. Brush any sugar crystals off the side of the pan with a wet pastry brush. Remove from the heat and carefully whisk in the warm cream mixture (the mixture will bubble). Add the chocolate and stir until smooth.
Whisk the egg yolks in a medium bowl. Whisk about half of the caramel into the yolks, then add the remaining caramel and whisk until smooth. Strain through a fine-mesh sieve into a large liquid measuring cup.
Divide the mixture among six 6-ounce ramekins. Set the ramekins in a large baking dish, then add enough hot water to come about halfway up the sides of the ramekins. Cover the pan tightly with foil and bake until the pots de creme are set around the edges but still jiggle in the center, 45 to 50 minutes.
Remove the ramekins from the water and let cool to room temperature. Cover with plastic wrap and refrigerate until cold, at least 2 hours or overnight. Sprinkle with salt.