In a stand mixer with the dough hook and the warmed milk. Sprinkle yeast and 1/2 tsp sugar, mix them and let the mixture froth for 5-10 min. It should get bubbly
Add the remaining sugar, eggs, butter, 2 cups flour and salt. Beat until combined
Add the remaining flour and beat on medium high until the dough starts pulling off from the sides around 5-7 mins
You want a soft slightly sticky dough, if too wet add up to 2tbsp flour slowly
Form dough into a ball and turn it out onto a lightly floured surface. Knead for 2 minutes, then place into a greased bowl
Cover the bowl with plastic wrap and let it rest for an hour, or until it has doubled in size
Once it has doubled, punch the dough to release any air bubbles and place it onto a lightly floured surface. Roll out the dough into 2cm thickness
With a doughnut cutter, cut out 12 doughnuts. Place them on baking paper and cover with a towel. Let them rest for 20 mins. While waiting, 10 mins thru resting, place a pot on your stove, fill with vegetable oil and turn the heat on high, You want reaaaally hot oil (190C) so you don't end up with oily doughnuts
Place three doughnuts at a time, frying for a min on each side. Remove and place on kitchen towel to absorb excess oil