Preheat the oven to fan assisted 160C / 180C / 350F / gas 4 and lightly oil a 6 cup doughnut tin.
Mix together the flour, sugar, baking powder and salt in a large bowl and set aside.
In another bowl, combine the buttermilk, eggs and Baileys before adding in the melted butter.
Mix the wet ingredients into the dry ingredients and stir until everything is just combined.
Using a spoon, add the batter in the doughnut cups until they are three quarters full.
Bake the doughnuts for 13-15 mins until a toothpick comes out clean, remove them from the oven and let them cool in the pan before transferring them to wire rack to cool completely.
Make the glaze when the doughnuts are cool.
Add the icing sugar and 2 tbsp of baileys into a bowl and whisk with a fork to combine. Add another tbsp of Baileys as necessary so you end up with a thick but dipable glaze.
Dip the doughnuts into the glaze, top with sprinkles and allow the glaze to set for 30 mins before serving.
Notes
I actually get 7 donuts form this recipe. Basic doughnut recipe adapted from Joy the Baker.