Warm up the milk so that it is warm to the touch but not hot and add to a bowl, stir 1 teaspoon of sugar and the yeast and let sit till foamy.
Add the rest of the sugar, the salt, egg, and melted butter while stirring. Once combined, slowly add in the flour while stirring, once added knead for about 5 minutes until the dough is elastic and smooth.
Grease a bowl and put the dough into the bowl, let it rise for roughly 30-45 minutes or until the dough has doubled.
Turn the dough out onto a floured surface, punch it down, and then roll it out to about 1/2 inch thickness. Cut out the donuts using a 3 inch cutter for the outside and a 1 inch cutter for the center, you can also use glasses or cups.
Once cut out, transfer the donuts and donut holes to a lightly floured parchment paper and let rise for another 20-30 minutes.
Once the donuts have risen, heat up some oil and fry the donuts, once fried, coat in whatever toppings or glaze you want.