In a large bowl, combine flour, sugar, and yeast.
Warm the milk and butter until melted, then let cool slightly.
Add the milk mixture, eggs, and vanilla to the dry ingredients.
Mix until a dough forms.
Knead the dough on a floured surface for about 10 minutes.
Place the dough in a greased bowl, cover, and let it rise for 1 hour.
Roll out the dough to about 1/2 inch thick.
Cut out circles using a cookie cutter.
Place filling in the center of half the circles, then top with remaining circles.
Let rise for another 30 minutes.
Heat oil in a deep fryer to 350°F (175°C).
Fry bomboloni until golden brown on both sides.
Drain on paper towels and dust with powdered sugar.