Prepare the Dough:

1. Activate the Yeast: In a small bowl, combine the lukewarm milk, sugar, and yeast. Stir to dissolve the sugar, then let the mixture sit for 5-10 minutes until it becomes foamy.
2. Mix Dry Ingredients: In a large mixing bowl, whisk together the flour and salt.
3. Combine Wet Ingredients: Add the yeast mixture, eggs, butter, vanilla extract, lemon zest (if using), and rum (if using) to the flour mixture. Mix everything together until a dough starts to form.
4. Knead the Dough: Turn the dough onto a floured surface and knead for about 10 minutes, until it becomes smooth and elastic. You can also knead using a stand mixer with a dough hook attachment for 6-7 minutes on low speed.
5. First Rise: Place the dough in a greased bowl, cover it with a clean towel or plastic wrap, and let it rise in a warm place for 1-1.5 hours, or until it doubles in size.

Make the Pastry Cream (if using):

6. Prepare the Pastry Cream: In a saucepan, heat the milk over medium heat until it just begins to simmer. In a separate bowl, whisk together the egg yolks, sugar, and cornstarch. Slowly pour the hot milk into the egg mixture while whisking constantly. Return the mixture to the saucepan and cook over medium heat, whisking constantly until it thickens, about 3-5 minutes. Remove from heat and stir in the vanilla extract. Let it cool to room temperature before filling the donuts.

Shape and Fry the Bomboloni:

7. Shape the Donuts: Once the dough has risen, punch it down and turn it out onto a floured surface. Roll the dough out to about ½-inch thickness. Use a round cookie cutter or a glass to cut out circles of dough.
8. Second Rise: Place the dough circles on a parchment-lined baking sheet, cover them with a clean towel, and let them rise for 30 minutes until they puff up.
9. Heat the Oil: Heat a large pot of vegetable oil to 350°F (175°C) for frying. You’ll need enough oil to submerge the donuts completely.
10. Fry the Donuts: Carefully drop the dough circles into the hot oil, a few at a time, being sure not to overcrowd the pot. Fry the donuts for about 2-3 minutes on each side, until they are golden brown and cooked through. Remove from the oil and drain on a paper towel-lined plate.
11. Dust with Powdered Sugar: While the Bomboloni are still warm, dust them generously with powdered sugar.

Fill the Bomboloni:

12. Fill the Donuts: Use a pastry bag or a small spoon to inject the cooled pastry cream, jam, or Nutella into the center of each donut. You can use a long, thin piping tip to insert the filling or gently slice the donuts open if you prefer.

Serve:

13. Serve Immediately: Serve the Bomboloni fresh and warm, and enjoy the sweet, creamy filling inside each donut.