For the Cream Puffs:

1. Preheat oven to 425°F. Line two baking sheets with parchment paper or silicone mats.
2. Combine the butter and water in a medium saucepan. Bring to a boil. 
3. While they are heating, whisk together the flour, sugar, and salt in a small bowl.
4. Once the butter has melted completely, reduce the heat to low and add the flour mixture. With a sturdy wooden spoon, vigorously stir until the batter forms a pasty, gluey dough, about 5 minutes.
5. Transfer the batter to a bowl of a stand mixer fitted with the paddle attachment. On medium speed, mix the dough for 5 minutes to slightly cool it. 
6. With the mixer still running on medium speed, add one egg at a time. Wait until the egg is completely mixed in before adding another. Mix in the vanilla until completely incorporated. The mixture should now be smooth, glossy, and slightly thick.
7. Use a small cookie dough scooper to create 12 mounds of dough about 1 1/2 inches wide and distribute them onto one of the prepared baking sheets, leaving about 2 inches of space between each mound. Repeat with the other baking sheet and the rest of the dough.
8. Bake for 20 to 25 minutes, until golden and puffed. Let the shells cool completely on the baking sheets before filling.

To Assemble:

1. Once the puffs have completely cooled, use a sharp petty knife to carefully cut around the middle of each cream puff horizontally, stopping about 75% of the way through. The pastry should still remain intact, with enough of an opening for the pudding.
2. Use a small spoon to carefully place about a tablespoon of pudding inside each partially cut pastry. For a more controlled process, you can transfer the pudding to a piping bag fitted with a small circular tip and pipe the filling into each pastry. 
3. To melt the chocolate, place the finely chopped chocolate in a small, microwave-safe bowl. Heat in the microwave at 30-second intervals, stirring between each interval with a spatula, until completely melted. If your chocolate has seized, don’t panic! Follow our advice on how to quickly save it. 
4. Drizzle or spread the melted chocolate over the top of each pastry. Serve immediately.