Preheat the oven to 180°C/Fan 160°C/Gas 4 and line a large baking sheet with baking parchment. Place the butter, sugar and 125ml of water into a small saucepan over a medium heat.
Bring the mixture to a rolling boil and when all the butter has melted, add the flours and vigorously beat with a wooden spoon until a smooth ball of dough forms.
Keep the pan on the heat and stir rapidly for a further minute to cook the flour. Tip the dough into a bowl and leave it to cool until it has stopped steaming; it needs to cook properly so that when you add the eggs they won't scramble.
Beat the eggs together in a jib, then add to the cooled dough in three separate additions, beating well with a wooden spoon.
You might not need to add all the egg – when adding the final amount you want to add just enough so the dough falls off the spoon and leaves a 'v' shape.
Spoon the pastry into a large piping bag fitted with an open star nozzle. Using the star nozzle helps the choux pastry expand in a more even way.
Line a ruler up next to the baking sheet and pipe 12 x 10cm éclairs onto the sheet, making sure to leave enough space between each one for them to expand during baking.
Use a wet finger to smooth over any bumps. Glaze each éclair with the egg using a pastry brush.
Bake for 25–30 minutes until golden brown and well risen. Turn the oven off and leave the éclairs in the oven to dry out and cool completely.
Whip the mascarpone and cream together with the Baileys until it thickens, then spoon this mixture into a piping bag. Use a skewer to pierce the cooled éclairs at one end and fill with the Baileys cream.
To make the topping, add the coffee to the icing sugar a little bit at a time until you get a paste that is just thick enough to spread onto the eclairs without it dripping down the sides.
Dip the éclairs top down into the icing or use a small palette knife to spread it over each one then dust with cocoa powder. These are best served as soon as possible, as the cream will make the pastry soft.