Make the Choux buns1. Preheat the oven to 200c. Very lightly oil a large flat baking tray.
In a small saucepan combine the water and butter. Place over a low heat until the butter is melted, then increase the heat to high and briefly bring to a rolling boil. Remove from the heat, quickly pour in the flour in one go and mix vigorously until smooth and the dough comes away from the sides to form a ball. Transfer the dough to a mixing bowl and spread out into a thin layer to help cool it down.
Once the dough is no longer hot, add the beaten eggs, a little at a time, beating well between additions until a dropping consistency is achieved. You may not need all of the egg.
Transfer the choux mixture to a piping bag fitted with a 1cm nozzle and pipe small buns 3cm apart directly onto the baking tray. Gently pat down any peaks and bake for 20 minutes until puffed and golden. Use a skewer to poke a small hole into each of the choux buns, and return to the oven upside down for 2-3 minutes. This allows the steam to escape, helping to dry out the buns and results in a crisp and light shell for filling.
Transfer the cooked choux buns to a wire rack and set aside to cool while you prepare the filling and sauce.
NOTE: Choux buns can easily be made ahead of time. Cooked buns can be frozen for up to 2 months. When ready to serve, simply thaw at room temperature and briefly refresh in a hot oven for several minutes to crisp up.
Make the Chocolate Sauce: In a small heatproof bowl, combine the cream, chocolate, Baileys and sugar and heat over a pan of gently simmering water until smooth. Set aside to cool.
Make the Chocolate Cream Filling: In a large bowl, combine the cream, Baileys and Icing Sugar. Whisk to soft peaks and transfer to a piping bag.
To assemble: Fill the cooled choux buns with the chocolate cream, drizzle with chocolate sauce and serve immediately.