Check the instructions on your yeast packet. Some yeast can be added directly to the dry ingredients, while others need to be activated in a little warm liquid first. If activating, use a bit of the lukewarm milk from the recipe.

In the bowl of a stand mixer fitted with the dough hook, combine the bread flour, 00 flour, and sugar. Add the softened butter cubes, then pour in the eggs, lukewarm milk, vanilla, and salt.

Knead on low speed (KitchenAid speed 2) for 10 minutes, until the dough is smooth, elastic, and slightly tacky to the touch. If using cups, the dough should be tacky, not wet or sticky—if too wet, add a tablespoon of flour at a time.

Turn the dough out onto a clean, unfloured surface. Gently knead 2-3 times to form a smooth ball. Place in a lightly oiled bowl, cover with plastic wrap, and let rise for 2-3 hours, or until tripled in size.

Once risen, turn the dough out onto a clean surface, punch it down to release the air, and knead a few times to bring it back into a smooth ball. Flatten with your hands, then roll into a rectangle 1/2 inch (1.5 cm) thick.

Using a 3.5-inch round cookie cutter or a glass, cut out doughnuts. Gather the scraps, re-knead, and re-roll to cut more. Place the cut doughnuts on a parchment-lined baking sheet, cover loosely with plastic wrap, and let rise for 1 to 1.5 hours, until tripled in size.

While the doughnuts are rising, prepare the pastry cream (see below) and let it cool completely.

When ready to fry, heat vegetable oil in a deep, heavy pot to 340°F (170°C). The oil should be about 3 inches deep. Line a plate with paper towels and have a bowl of superfine sugar ready.

Cut the parchment into squares so each doughnut sits on its own piece. Carefully lower each doughnut into the hot oil, parchment side up, then immediately remove the parchment with tongs. Fry in batches without overcrowding the pan.

Fry for 2 minutes on the first side, then flip and fry for another 2 minutes, until deep golden brown. Remove with a slotted spoon and drain on paper towels for about 2 minutes. While still warm, roll in the sugar to coat evenly. Cool completely before filling.

To fill the bomboloni, use a small knife to make a small incision in the side of each cooled doughnut, gently moving the knife to create a pocket.

Fit a piping bag with a small round tip and fill with the cooled pastry cream. Insert the tip into the incision and pipe the cream until it starts to bulge slightly. Repeat with all doughnuts.

Serve immediately for best texture, or store in an airtight container at room temperature for 1-2 days. For longer storage, refrigerate the filled doughnuts, but let them come to room temperature before serving.

In a large bowl, whisk together the egg yolks, sugar, vanilla, and lemon zest until well combined. Add the cornstarch and whisk until smooth and lump-free.

In a saucepan, heat the milk over medium heat until hot but not boiling. Remove from heat and let sit for 1 minute. Slowly pour the hot milk into the egg mixture, whisking constantly to prevent the eggs from scrambling.

Return the mixture to the saucepan and cook over low heat, stirring constantly with a wooden spoon or whisk, until it thickens and becomes very creamy, about 10-15 minutes. Do not increase the heat, or the eggs may scramble.

Once thick, remove from heat and pour into a clean bowl. Press plastic wrap directly onto the surface of the cream to prevent a skin from forming. Let cool completely at room temperature, then refrigerate until ready to use.