In a large mixing bowl, combine all-purpose flour, salt, and granulated sugar. Create a well in the center, then pour in warm milk and fresh yeast. Let the yeast activate for about 5-10 minutes until it's bubbly.

Incorporate softened butter and beaten eggs until the mixture is homogenous. Knead the dough for approximately 8 minutes until it's smooth and elastic.

Shape the kneaded dough into a ball and place it in a greased bowl. Cover with a clean kitchen towel or plastic wrap, and let it rise in a warm environment for about 90 minutes until doubled in size.

Turn the risen dough out onto a lightly floured surface. Roll out to a thickness of about ½ inch and cut out circles using a round cutter. Place them on a floured baking sheet and let rest for about 10 minutes.

In a deep frying pan, heat vegetable oil to 350°F (175°C). Carefully add the rested dough rounds and fry until golden brown on both sides, about 2-3 minutes per side. Remove using a slotted spoon and drain on paper towels.

In a saucepan, heat whole milk over medium heat. In a separate bowl, whisk together egg yolks, sugar, and cornstarch until smooth. Gradually combine with the hot milk, stirring until thickened, about 5-7 minutes. Stir in vanilla extract and cool.

Cut a small slit into the side of each bombolone and fill with the prepared custard. Dust with powdered sugar and serve warm or at room temperature.