Prepare the chocolate: Place the chopped chocolate in a medium heatproof bowl.
Make a cornstarch and egg slurry: Put the cornstarch and salt together in a medium bowl and whisk to make sure there are no lumps. Slowly whisk in the cream, making sure there are no lumps. (To be really sure, reach into the bowl and gently rub out any lumps between your fingers.) Whisk in the egg yolks.
Warm the milk: In a 3-quart (2.8-L) saucepan over medium heat, whisk the sugar into the milk. Warm for 3 to 5 minutes, until the sugar dissolves, bubbles form around the edges, and the entire surface of the milk begins to quiver. Turn off the heat.
Temper the slurry: Pour 1 cup (240 ml) of the hot milk into the bowl with the slurry, whisking constantly. The mixture should come together smoothly, with no lumps. If you see any, add a little more liquid and whisk them out. Pour it back into the pan, counting to 10 and whisking constantly as you pour.
Thicken the pudding: Turn the heat back on to medium and bring the mixture to a simmer, whisking frequently and vigorously, working all the angles of the pot and scraping the bottom. Continue whisking for about 5 minutes, until the custard becomes very thick and starts to boil, with large bubbles that slowly pop up to the surface. Boil for 2 minutes, whisking constantly.
Flavor the pudding: Turn off the heat and stir in the vanilla extract. Stir the chocolate into the pudding and let sit for 2 to 3 minutes. Whisk gently until the pudding is smooth and glossy and has fully absorbed the chocolate.
Chill the pudding: Immediately pour the hot pudding into a shallow container. Place plastic wrap or buttered wax paper directly on the surface of the pudding (if you don't like pudding skin). Cover and refrigerate.