In a large mixing bowl, combine the all-purpose flour, sugar, and instant yeast. Gently warm the milk until it reaches about 110°F, then add it to the dry ingredients along with the eggs, melted butter, and vanilla extract. Mix until combined, then knead the dough on a floured surface for about 8-10 minutes until it's smooth and elastic.

Place the kneaded dough in a lightly greased bowl, covering it with a damp cloth or plastic wrap. Allow it to rise in a warm, draft-free area for 1-2 hours, or until it has doubled in size.

Once the dough has risen, punch it down to release the air. Turn it out onto a floured surface and roll it out to about 1-inch thickness. Cut out small circles using a round cutter, then roll each piece into a ball and place them on a flour-dusted tray.

Cover the tray with a clean kitchen towel and let the shaped bomboloni rise for 30-45 minutes.

In a deep pan, heat vegetable oil to approximately 360°F. Carefully add a few bomboloni at a time, frying them for about 2-3 minutes on each side until golden brown. Use a slotted spoon to remove and drain on paper towels.

Allow the bomboloni to cool for a few minutes before filling them. Using a pastry bag fitted with a nozzle, inject the creamy custard filling into each warm donut.

Finally, roll the filled bomboloni in powdered sugar for an extra touch of sweetness. Serve warm.