In a large bowl, whisk together flour, sugar, yeast, and salt.
In a separate bowl, whisk together eggs and milk. Pour into the dry ingredients.
Mix until a shaggy dough forms. Add the melted butter and knead for 8-10 minutes until the dough is smooth and elastic. You can use a stand mixer with a dough hook.
Place the dough in a lightly oiled bowl, cover with plastic wrap, and let it rise in a warm place for 1-1.5 hours, or until doubled in size.
Punch down the dough and divide it into 12 equal pieces. Roll each piece into a ball.
Place the dough balls on a lightly floured surface, cover, and let them rest for another 30 minutes.
Heat the vegetable oil in a deep pot or Dutch oven over medium heat to 350°F (175°C).
Carefully fry the dough balls in batches for 2-3 minutes per side, until golden brown.
Remove the doughnuts with a slotted spoon and drain on paper towels.
In a shallow dish, combine sugar and cinnamon (if using). Toss the warm doughnuts in the sugar mixture until coated.
If filling, let the doughnuts cool slightly, then use a piping bag to inject pastry cream into the center.
Notes
Bomboloni are best enjoyed fresh. They can be stored in an airtight container at room temperature for up to 2 days, though they may lose some of their crispness.