In a large mixing bowl, whisk together the eggs, sugar, salt, vanilla, oil, and melted butter. Add 2/3 of the flour and mix with a whisk.

Add the milk and yeast mixture and stir with a spatula until the dough is fairly smooth, then add the remaining flour and mix well with the spatula.

Transfer the very sticky dough (this is normal) onto a well-floured work surface. Knead the dough for about 10 minutes until it no longer sticks. Add more flour if needed.

Place the dough in a bowl, cover with a cloth, and let it rise at room temperature for 1 hour 30 minutes, until doubled in size.

Punch down the dough. Roll it out to 1/2 inch thick and use a 2 1/2 or 3 inch round cutter to cut out the donuts. Gather the scraps, form a ball, and repeat until all the dough is used.

Fry the donuts in a deep fryer or a pot of hot oil heated to 320–340°F (160–170°C). Fry each side for 2 minutes.

Transfer the donuts to a plate of granulated sugar and roll them to coat.

Set them aside on a plate. Fill with your choice of jam, fruit compote, or chocolate spread.

Use a piping bag with a tip, fill it with your chosen filling, and make a hole in the side of each donut to generously fill them.

Arrange in a basket and enjoy!