Prepare the dough: Whisk the flour, sugar, salt, and yeast together in a bowl.
Add in the warmed milk, warmed buttermilk and melted butter.
Knead the dough: Knead the dough for about 2 minutes using a mixer with a dough hook attachment. It will still be sticky after 2 minutes Turn out the dough onto a well-floured surface and knead it by hand for another 2 minutes. You can add up to an extra tablespoon of flour while kneading to get a smooth soft dough. If you do not have a mixer, then just knead the dough by hand on a well-floured surface for just 3 to 5 minutes until it forms a soft dough Do not over handle the dough.
Leave the dough to rise: Cover the dough with plastic wrap and leave to rise for 45 minutes in a warm, draft-free area of your kitchen.
Punch down the dough: After the dough has risen, punch it down and turn it out of the bowl onto a well-floured surface. Knead for 1 minute.
Roll out and shape the dough: Use a rolling pin to roll out the dough to about 1 inch (2 cm) thick. Cut the dough with a cookie or doughnut cutter. Place doughnuts onto a baking sheet, then lightly cover and allow to rest for 5 minutes while the oil heats up.
Fry the doughnuts: Turn the stove up to medium-high heat. Place a heavy-based pan with sufficient oil to deep fry the doughnuts. Allow the oil to heat up to between 350°F – 370°F ( 176°C – 185°C ) before frying the doughnuts. Carefully drop the doughnuts into the oil and fry for about 1 ½ minute on each side until golden brown and cooked. Remove the cooked doughnuts from the oil and place it on a sheet of paper towel while you make the glaze.