How to Make It
Preheat the oven to 400°. Line 2 large baking sheets with parchment paper.
In a large saucepan, bring the milk, water, 1 stick of the butter and the salt to a boil over high heat. Add the flour and remove from the heat. Stir until the dough forms a shiny mass. Using a mixer, beat the dough at low speed for 2 to 3 minutes, just until slightly cooled. Increase the speed to medium and beat in the eggs, one at a time, beating well between additions; be sure to scrape down the saucepan.
Transfer the dough to a pastry bag fitted with a 3/4-inch plain tip. Pipe twelve 1 1/2 inch mounds onto each sheet. Using a moistened finger, round the tops of the dough. Bake for about 25 minutes, until the puffs are golden, shifting the sheets halfway through.
Poke a 1/4-inch-deep hole into the side of each puff and return them to the oven. Turn off the oven, leave the door ajar and let the puffs cool and dry out for 2 hours.
Meanwhile, in a bowl, using a mixer, beat 1 1/2 cups of the cream with the confectioners' sugar until firm. Beat in the vanilla extract.
Cut off the top third of each puff and scoop out the soft dough in the center. Spoon the cream into the puffs, replace the tops and stack them on a plate. Chill for 10 minutes.
In a small saucepan, bring the remaining 3/4 cup of heavy cream just to a boil. Remove from the heat. Add the chocolate and the remaining 1 tablespoon of butter and let stand just until the chocolate is melted. Whisk until smooth. Drizzle some of the chocolate sauce over the puffs and serve, passing the remaining sauce on the side.