Using a large bowl, combine the instant dry yeast, sugar, flour, and salt. ( Dry ingredients )
In a jug or saucepan, warm the milk and water. It should be just warm, not too hot or cold. If you have a thermometer, it should read between 100° - 115°F ( 37°C - 46°C)
Add beaten eggs, shortening, or butter to the warm milk and water mixture ( wet ingredients).
Add the wet ingredients into the bowl with the dry ingredients and mix to combine.
Turn out onto a floured surface, and knead for about 3 to 5 minutes until the dough is soft and smooth. If you find that the dough is too sticky, then add up to ¼ cup extra flour while kneading.
Place the dough back into the bowl and in a warm, draft-free area of your kitchen, allow the dough to double in volume. This should take an hour.
After an hour, punch down the dough and turn it out onto a floured surface. Using your palms press out the dough to about ½ inch ( 1 ½ cm ) thick and cut out the doughnuts using a doughnut or cookie cutter. If you are using a cookie-cutter, then cut out the center of each doughnut using a smaller cutter as well.
Place the cutout doughnuts onto a tray and leave to rise again for about 15 to 20 minutes.
Using a deep pan or pot, add sufficient oil to deep fry the doughnuts.
Allow the oil to heat up to between 350°F - 370°F ( 176°C - 185°C ) before you start to fry the doughnuts.
Deep fry the doughnuts for about 1 minute on each side, until cooked and golden brown.
Transfer the doughnuts to a plate lined with a paper towel
Top or frost as preferred
Topping suggestion : cinnamon sugar, melted chocolate, glace icing.