- With the rack in the middle position, preheat the oven to 400°F (200°C). Line a baking sheet with parchment paper.
- In a saucepan, bring the water, butter, sugar and salt to a boil. Remove from the heat. Add the flour, all at once, and stir vigorously with a wooden spoon until the dough forms a smooth ball and pulls away from the walls.
- Place the pan over low heat and cook, stirring, for about 2 minutes. Remove from the heat and let cool for a few minutes.
- Add the eggs, one at a time, beating vigorously with an electric mixer or wooden spoon after each addition, until smooth.
- Transfer to a pastry bag fitted with a 1/2-inch (1 cm) plain tip. Pipe small rounds, with about 2 tbsp of dough each, on the baking sheet. Gently brush with the beaten egg.
- Bake until the puffs are golden brown, about 20 to 25 minutes. Turn the oven off, prop the door ajar with a wooden spoon and let sit for 15 minutes. Remove from the oven and let cool completely on the baking sheet.
Cream Fudge Sauce
- In a saucepan, off the heat, combine the brown sugar and cornstarch. Add the cream and bring to a boil, stirring constantly with a whisk. Simmer for 1 minute. Stir in the vanilla.
- To serve, cut each profiterole in half crosswise, fill with a scoop of ice cream, replace the top and drizzle with hot cream fudge sauce.
The puffs can be made ahead and frozen once baked. To thaw, place them in the oven at 350°F (180°C) for a few minutes.