Make the dough: In the bowl of a stand mixer, use your fingers to dissolve the yeast into the warm water. Stir in 10 grams (1 tablespoon) of the flour and 5 grams (1 tablespoon) of the sugar, and set aside until the mixture is bubbling, about 15 minutes.

Add the egg yolks, whole egg, warm milk, orange zest and juice, brandy (if using), salt, vanilla, the remaining sugar, and the flour to the yeast mixture. Attach the dough hook and mix on low speed until the dough comes together, 1 to 2 minutes.

With the mixer running on medium speed, gradually add the butter, a pinch at a time. Continue to mix until the dough pulls away from the sides of the bowl (add a few spoons of flour if needed), is smooth and shiny, and is beginning to climb up the dough hook. This will take about 4 minutes.

Stretch and fold the dough, then let it rise: Turn the dough out onto a lightly floured work surface and lightly dust the top of the dough with flour. Stretch the top piece of the dough until it tears, then fold it on top of the center. Give the dough a quarter turn and repeat, tearing and folding, adding more flour as needed, until the dough isn’t sticky, 2 to 3 minutes. Transfer the dough to a lightly floured bowl, sprinkle the top with flour, and cover the bowl with plastic wrap. Set it aside in a warm and draft-free spot until the dough has doubled in volume, about 1 hour.

Roll and stamp the dough: Set the dough on a lightly floured work surface, and use a rolling pin to roll it into a ½-inch-thick sheet. Use a 2½-inch round cookie or biscuit cutter to stamp out rounds of dough. Stamp them out as close together as possible to minimize the amount of scraps; after pressing the cutter into the dough, twist it before pulling it out from the sheet of dough (to help strengthen the seal so the doughnut puffs nicely during frying). Gather the scraps; press them together; rest for 5 minutes, covered; and then gently reroll them to stamp out a few more sufganiyot. Discard the remaining bits of scraps.

Let the dough proof: Place the dough rounds on a lightly greased (use a little oil) parchment paper–lined sheet pan and cover with a kitchen towel. Let the dough rise in a draft-free spot at room temperature until nearly doubled in volume, 40 to 50 minutes. (At this point, after rising, the dough can be refrigerated for up to 3 hours before frying.)

Fry the dough: Fill a large saucepan with enough oil to reach a depth of 4 inches. Heat the oil over medium-high heat until it reads 350°F on an instant-read thermometer. Start with one sufganiya and fry, turning it with a slotted spoon or frying spider, until both sides are golden, about 2 minutes. Use the spider or slotted spoon to transfer the doughnut to a paper towel–lined plate or sheet pan. Continue frying the remaining doughnuts in batches, taking care not to crowd the pan; otherwise, the oil will cool and the doughnuts will absorb more oil and become greasy. Let the doughnuts cool completely before filling them.

Fill the sufganiyot: Place the jam in a food processor and process until smooth. Scrape the jam into a piping bag fitted with a ¼-inch round tip and insert the tip into the top of a doughnut. Squeeze jam into the doughnut until the jam begins to ooze out of the hole at the top. Repeat with the remaining sufganiyot. Sprinkle with confectioners’ sugar before serving.