In a small bowl, combine the warm milk and yeast. Allow it to sit for about 5-10 minutes until it becomes frothy.

In a large mixing bowl, combine the flour, sugar, and salt. Make a well in the center, and add the egg yolks, vanilla extract, and activated yeast mixture. Mix until combined.

Add the softened butter to the mixture, and knead on a floured counter for about 8-10 minutes until the dough is smooth and elastic. Place the kneaded dough in a greased bowl, cover, and let it rise in a warm place for about 1 hour.

Once the dough has doubled in size, punch it down and roll it out to a ½ inch thickness. Cut into circles using a donut cutter or a glass. Place the circles on a floured baking sheet, cover them with a cloth, and let them rise for another 30 minutes.

Heat vegetable oil in a deep skillet or fryer to about 350°F (175°C).

Carefully drop a few donuts into the hot oil, frying them for about 2-3 minutes on each side or until golden brown. Remove with a slotted spoon and set on paper towels to drain excess oil.

Allow the Bomboloni to cool slightly before filling them with your desired filling using a piping bag. Finally, roll them in powdered sugar before serving.