Preheat the oven to 170°C/325°F. Lightly grease a doughnut pan with oil
In a large bowl, beat the milk, sugar, Irish cream, cooled butter and egg together.
Sift in the flour, baking powder and cocoa powder and gently combine.
Fill the doughnut moulds with the batter until ¾ full and bake for 15 minutes, or until springy and a skewer inserted in the middle comes out clean.
Leave to cool in the pan for 5 minutes, then carefully transfer to a wire rack to cool completely.
For the Irish Cream Glaze
Beat the sugar and Irish cream together until smooth. It should reach a thick drizzling consistency. If necessary, add a teaspoon more of icing sugar to thicken or a teaspoon of water to thin.
Pour it into a shallow bowl and dip in the completely cooled doughnuts to cover one side. Add sprinkles if desired. Set aside to set.