Pour warm milk over butter and vegetable shortening and leave to melt.
Mix dried yeast with warm water and leave for 5 minutes until frothy. Water can't bee too hot or too cold (between 35-45C).
In a big bowl (or a mixer) combine all ingredients for the dough and mix together. Once it starts becoming more like a dough, start kneading or use mixer with dough attachment for about 5 minutes.
Transfer to oiled bowl, cover loosely with cling film or a tea towel and leave to rest in warm, cozy place for about an hour.
Once the dough doubled in size, knead once more and roll with a pin to form a 2.5-3cm thick disk. You might need to use some flour for the surface before you roll it. Cut out the donuts and put on the floured baking trays. Leave in a warm place for about 30 min.
10 minutes before donuts are risen, start heating the oil. It should reach about 190C. I usually check the temp with potato cut in half - when it is frying nicely - the oil is ready.
Fry donuts for about a minute on each side until golden. Transfer to the dish lined with kitchen paper to cool. Don't try to fry more than 2-3 at a time.
Simply mix all icing ingredients together. You can leave it to cool and thicken a little or you can dip the donuts straight away.
When you cut out the donut centres, do not throw these out! Fry them the same way as the rest of the donuts:)