Heat oven to 325 F. Coat a doughnut pan with non-stick cooking spray & set aside.

Whisk flour, cocoa, baking soda, espresso powder and salt in a large bowl.

In a smaller bowl, whisk together buttermilk, Baileys, sugar, egg, oil and vanilla until smooth. Add the milk mixture to the flour mixture and whisk until well blended.

Spoon the batter into a piping bag or a large resealable plastic bag. Cut the end or the corner and squeeze batter into prepared doughnut pan about 2/3 full. Bake for 10-12 minutes, until doughnuts spring back when lightly pressed. Cool in pan on rack for 3 minutes, then carefully turn out directly onto rack to cool.

Melt butter in a medium size pan over medium heat; once melted add the water, espresso and vanilla and whisk until combined. Slowly combine confectioner's sugar, adding the Baileys to thin out glaze. If the consistency is too thin, add a bit more sugar. If too thick add a bit more liqueur.

Dip doughnut tops in glaze and put on a rack to allow it to dry and slightly harden.