In a large mixing bowl combine 1 3/4 cups flour with yeast. In a saucepan heat milk, sugar, butter and salt until butter melts. Stir milk mixture into flour along with eggs, beating with a heavy-duty electric mixer on low for 30 seconds, just to combine. Increase speed to high and beat 3 minutes.
Add the remaining flour, a little at a time, stirring with a spoon to make a firm but pliable dough. Knead dough on lightly-floured work surface 4 to 5 minutes until smooth and supple. Transfer to an oiled bowl. Cover and let dough rise until it doubles in size, about 1 hour.
Turn dough out onto floured surface, punch down and roll out to 1 1/2 cm thickness. Cut out doughnuts with a floured doughnut cutter then re roll trimmings and cut them into doughnuts as well. Transfer doughnuts to baking trays, cover and let rise 45 minutes.
Heat oil in a deep-fryer to 180 degrees C. Fry doughnuts, in batches, turning several times, until golden all over. Using a slotted spoon remove doughnuts to a rack to drain. Let doughnuts cool and dredge in icing sugar.