In a large bowl or a bowl of a standing mixer, pour 1/2 cup of the milk then sprinkle the yeast and one tablespoon of the sugar. Let sit for 10-15 minutes until frothy.
To the yeast mixture, add the flour, salt, rest of the sugar mix using the paddle attachment on low, while drizzling the rest of the milk, melted butter and egg.
Once you have a shaggy mass, with no dry flour, replace the paddle attachment with the hook attachment and mix on medium speed until the dough is smooth and sticky and cleans the sides of the bowl.
Place the dough in a greased large bowl, grease the top then cover with plastic wrap for about 90 minutes, until doubles in size.
Punch the dough to release the air, divide the dough into ten pieces, roll each piece into a ball, and place it over a 4x4-inch parchment paper.
Place at a warm place for about two hours, until double in size.
In a large and wide pan, pour the oil and heat it to 320F (160C).
Carefully add 3-4 donuts (do not overcrowd) and fry for three minutes on each side.
Use a slotted spoon to invert the donuts into a plate lined with paper towels. Let them rest for 10-15 minutes.
Generously dust the donuts with the powdered sugar, and use a piping bag to fill the donuts from the top with the preserve, or your choice of filling. Serve immediately.