Add water and yeast together in a your stand mixer and set aside for 10 minutes.
Add in the milk, sugar, salt, eggs, shortening and half of the flour.
Turn the stand mixer on medium speed for 2 minutes, then add in the rest of the flour and mix until just combined. Take the bowl out of the stand mixer and cover with a clean towel to let it rise for an hour.
Working with half the dough at a time, roll it to around 1cm thick on a floured surface. Using two sizes of cookie cutter for the doughnut and it’s hole, cut out 6 doughnuts with each half of the dough and put onto a tray lined with baking paper. Leave to prove, covered, in a warm spot for 30-45 minutes.
Meanwhile make the glaze by adding the icing sugar, milk and vanilla essence to a bowl and mixing until smooth.
In a deep saucepan, heat the vegetable oil to 190C degrees. Fry the doughnuts on each side for 90 seconds. Drain on a cooling rack until you finish cooking them all then dip into the glaze. Return to the cooling rack, glaze side up, to harden for 30 minutes.
To serve, use a bread knife to slice each doughnut through the middle and fill with a scoop of ice cream. Eat immediately.