Preheat the oven to 350°F (180°C).

For the choux pastry: Bring the water, butter (cut into pieces), and sugar to a boil. Remove from heat and add the flour all at once, stirring vigorously until you get a thick dough that pulls away from the sides of the pan.

Cook over low heat, stirring, until a thin film forms on the bottom of the pan. Let cool slightly.

Beat the egg. Off the heat, add the egg gradually, mixing vigorously. Continue until the dough is smooth and shiny.

Spoon small mounds of dough onto a baking sheet lined with parchment paper. Bake for 30 minutes.

For the pastry cream: Heat the milk in a saucepan. Add the split vanilla bean and let it infuse.

Separate the egg white from the yolk. Whisk the yolk with the sugar until pale, then add the flour.

Slowly pour the hot (not boiling) milk into the mixture. Pour everything back into the saucepan and cook over low heat, stirring constantly, until the mixture thickens. Once thickened, it's ready.

For the caramel: Heat the sugar with a little water and a few drops of lemon juice in a small saucepan, without stirring. When it turns an even amber color, it's ready.

To assemble: Cut the tops off the cream puffs, fill with pastry cream, then replace the tops after dipping them in caramel. Enjoy!