Sift the flour into a large mixing bowl and stir in the yeast, sugar and salt. Add the butter and rub into the flour until well distributed.
Make a well in the centre and drop in the egg and add most of the warm milk. Mix to a soft sticky dough adding the remaining milk if required.
Lightly dust the work surface with a little flour and turn out the dough. Knead for a few minutes until the dough has lost most of its stickiness. Take care not to add too much extra flour as you work it or the dough will become tough.
Shape into a ball and place in a large lightly oiled bowl. Cover and leave in a warm place for 1½ - 2 hours or until the dough has doubled in size.
Knock back the dough and tip it out into the work surface a lightly knead. Divide into 9 equal pieces and roll into balls. Place on a lightly oiled baking sheet. Loosely cover and leave in a warm place for about 30-45 minutes.
Heat the oil in a deep fat fryer to 170℃ (340°F). Carefully lower the doughnuts into the hot oil and cook in batches for 4-5 minutes turning until golden all over. Remove from the hot oil with a draining spoon and place on a tray lined with kitchen paper to drain.
Make the Irish cream filing
While the doughnuts are prooving, make the filling. Place the milk in a saucepan and heat until almost boiling.
Whisk the sugar, egg yolks cornflour and vanilla paste together in a large bowl. Gradually whisk in the hot milk until well combined. Return to the pan. Cook gently, stirring, until the mixture thickens.
Remove from the heat and return to the bowl. Add the butter and stir until melted Cover with a sheet of baking parchment and leave to cool, then chill until required.
When the doughnuts are cooked allow to cool slightly. Stir the Irish cream liquer into the cooled custard and spoon into a piping bag fitted with a plain nozzle.
Push the nozzle into each doughnut squeezing a little custard into the centre of each doughnut.
To make the coffee icing
Sift the icing sugar into a bowl and stir in enough coffee to make smooth icing. Dip each doughnut into the icing to coat the top of doughnut. Stand on a baking sheet or tray and allow to set.
To decorate if desired
Spoon the melted chocolate into a small piping bag and drizzle back and forth over the doughnuts before the icing has set. Top with a chocolate coated coffee bean and leave to set
CAUTION: Take extreme care when deep frying. Use a deep fat fryer if you have one. If cooking in a pan, never fill more than one-third full with oil and never leave unattended, even for just a moment. Take care not to drop the doughnuts into the hot oil by lowering them into the oil gently.Nutrition information is calculated using an online nutrition database - is approximate and is meant as a guideline only. (It does not include optional decoration.)