Step
1
Prepare the dough: Add the milk, yeast and ¼ teaspoon sugar to a small bowl and stir to combine. Let sit for at least 5 minutes to ensure the yeast becomes foamy and fragrant. (If the yeast does not become foamy and fragrant, it is not active, and you will need to try new yeast.)
Step
2
Meanwhile, to the bowl of a stand mixer fitted with the whisk attachment, add the flour, remaining ½ cup sugar and the salt and combine on low speed, about 1 minute. Switch to the dough hook attachment on your stand mixer, then add the yeast mixture, eggs, vanilla extract and zest to the bowl. With the mixer on low speed, knead until combined, scraping down the sides of the bowl as you go, until the dough comes together in a ball, about 2 minutes. With the mixer running, add one piece of butter at a time, allowing each piece a few moments to incorporate into the dough. After the last piece of butter is incorporated, continue kneading the dough for an additional 8 minutes, scraping down the sides of the bowl as needed.
Step
3
Turn the dough out of the mixing bowl onto a clean surface (do not add extra flour to the surface). Knead the dough 2 to 3 times, shaping it into a smooth ball. Place the dough in a clean bowl that is lightly greased with vegetable oil. Cover the bowl with plastic wrap or a clean dish towel and let the dough rise until triple its original size, about 3 hours.
Step
4
While the dough rises, make the cream filling: Combine the milk, eggs, sugar, cornstarch and lemon zest in a large pot and whisk until well combined. Place the pot over medium heat and cook, whisking continuously, for 6 to 10 minutes, until the cream starts to bubble and is very thick. Remove from the heat and add the butter and vanilla extract; whisk until incorporated and smooth. Set the filling aside to cool slightly, uncovered, then cover with plastic wrap directly touching the surface of the cream and refrigerate until cold, 2 to 3 hours. (Filling can be made 2 days in advance and kept refrigerated.)
Step
5
Just before the dough has finished rising, cut 12 (6-inch) squares out of parchment paper and place six each on two sheet pans or trays. Gather a rolling pin and a 3½-inch round cookie cutter (or use a drinking glass or jar). Turn the risen dough out of the bowl onto a clean work surface. (Do not add extra flour to the surface.) Roll the dough out until it’s ½-inch thick. Using the cookie cutter, cut out 12 dough rounds and gently place each on a square of parchment. You will need to re-roll the dough once or twice to use up all of the dough. Cover both sheet pans with plastic wrap and let rise for 1½ hours.
Step
6
Make the doughnuts: Line a baking sheet with paper towels; set aside. Fill a pot with 1½ to 2 inches of oil. Heat over medium until a deep-fry thermometer registers 350 degrees. Using the parchment square to help, carefully lower a dough round into the pan and quickly remove the parchment paper. Fry two dough rounds at a time (so as not to overcrowd the pan), for 2 minutes per side, until golden brown, maintaining the oil at 350 degrees between batches. Remove from the oil and let cool on the prepared baking sheet. While still warm, roll the doughnuts in granulated sugar and set aside to cool completely, about 45 minutes.
Step
7
Fill the doughnuts: When the doughnuts are cool, insert a small knife into the side of each doughnut and move the knife back and forth inside the doughnut to make a pocket. Attach a round tip to a pastry bag (see Tip) and fill with the cream filling. Pipe filling into the hole in each doughnut, until the doughnut is slightly inflated and cream begins to overflow from the hole. Serve immediately. (The bomboloni are best when eaten fresh, but once filled, they can be refrigerated in an airtight container for up to 2 days. Any leftover cream filling can be served topped with berries or ice cream or spread on toasted brioche as a bonus treat.)