In a large bowl, add yeast, ½ tsp. of sugar, and warm water, stir until well combined, then leave for 5 minutes until frothy.
Add milk, salt, egg, butter, and remaining sugar.
Gradually add flour while stirring continuously. Continue to add and stir until it begins to sit and gather in the middle of the bowl.
Transfer the dough to a floured surface and knead until the dough becomes elastic and smooth.
Once done, shape the dough into a ball, place it in a bowl, cover it with a kitchen towel, and leave it rising for 2 hours until the volume doubles.
Once risen, transfer the dough to a floured surface and roll it out using a rolling pin until ¼" thick. Then cut out donuts using a 3" diameter donut cutter, also cut from the center to make a hole.
Place the cut-out donuts on the pre-cut parchment papers and arrange them on a large tray. You can reuse the wasted dough to make more donuts.
Pour 3" of oil into a heavy-bottomed pan over medium heat. Carefully add the cut-out donuts to the hot oil without parchment paper and cook side for 2 to 3 minutes or until the color turns brown, then flip side and cook for 1 minute.
Once done, transfer the donuts to a large tray lined with a paper towel. Leave there until drained.
Finally, roll the donuts in the powdered sugar and serve.