Preheat the oven to 400°F (200°C) and set an oven rack in the middle position. Line a baking sheet with parchment paper.

In a medium saucepan, combine the water, milk, butter, sugar, and salt. Bring to a boil over medium heat, stirring occasionally, until the butter is fully melted.

Reduce the heat to low, add the flour all at once, and stir vigorously with a wooden spoon until the mixture forms a smooth ball and pulls away from the sides of the pan, about 1 minute.

Transfer the dough to the bowl of an electric mixer fitted with the paddle attachment. Let it cool for 5 minutes, then beat on low speed for 30 seconds to release steam.

With the mixer on low, add the eggs one at a time, beating well after each addition. Scrape down the sides as needed. Once all the eggs are incorporated, continue mixing for 1 minute more, until the dough is smooth, thick, and pipeable.

Transfer the dough to a piping bag fitted with a ½-inch (1.25-cm) round tip. Pipe 1¾-inch (4.5-cm) mounds onto the prepared baking sheet, spacing them 2 inches (5 cm) apart. Wet your fingertip and gently press down any pointed tips to prevent burning.

Bake for 22 to 25 minutes, without opening the oven until near the end of the baking time, until the puffs are golden and well-risen. Turn off the oven, crack the door open slightly, and let them sit inside for 30 minutes to dry out.

Transfer to a wire rack to cool completely.

In a small saucepan, heat the heavy cream over medium heat until steaming. Remove from heat and add the chopped chocolate and salt, stirring until smooth. Let it cool slightly before drizzling over the profiteroles.

For Ice Cream-Filled Profiteroles: Before assembling, scoop small balls of ice cream onto a parchment-lined baking sheet and freeze until firm. Once the profiteroles are completely cool, slice them in half horizontally using a serrated knife. Place a frozen ice cream ball onto the bottom half of each profiterole, then place the top half back on. Drizzle generously with the warm chocolate sauce and serve immediately.

For Pastry Cream-Filled Profiteroles: Before filling, whisk the chilled pastry cream until smooth. Using a small knife, poke a ¼-inch (6-mm) hole in the bottom of each profiterole. Transfer the pastry cream to a piping bag and pipe into each puff until almost filled. Drizzle with warm chocolate sauce and serve.