Preheat your oven to 425°F (220°C). In a saucepan, heat the butter and water together until the butter melts and the mixture boils. Remove from heat and stir in the sifted flour quickly until it forms a smooth ball and pulls away from the sides of the pan.
Let the dough cool slightly for 5 minutes. Then add the beaten eggs one at a time, stirring well after each addition until the mixture is smooth and glossy.
Line a baking tray with parchment paper. Using two teaspoons, drop small mounds of dough onto the tray, leaving space between each for expansion. Brush the tops lightly with the beaten extra egg for a shiny finish.
Bake in the hot oven for 10 minutes, then reduce the temperature to 375°F (190°C) and bake for another 15 minutes or until the profiteroles are puffed and golden. Avoid opening the oven door during baking to keep them from collapsing.
Whip the heavy cream until it forms soft peaks.
Heat the cream in a small saucepan until it just starts to simmer. Remove from heat and add the dark chocolate pieces. Stir until smooth and glossy.
Once the pastries are cool, slice them in half horizontally. Spoon or pipe the whipped cream into the bottom halves, then place the tops back on. Drizzle the warm chocolate sauce over the filled profiteroles before serving.
