Line 2 baking sheets with parchment paper and lightly dust the sheets with flour. Line 2 additional baking sheets with paper towels.
In the bowl of a standing mixer or in a large bowl, stir together warm milk, yeast, and 1 cup flour. Cover and set aside for 30 minutes. With a dough hook fitted to the mixer, and the motor on LOW, add eggs, evoo, vanilla extract, sugar, salt, and remaining flour. Alternatively, you can mix in ingredients by hand.
Knead by mixer or by hand until it’s smooth and elastic. If making doughnuts the same day, place dough in a lightly greased bowl and let rise for 1 to 2 hours until doubled in size. Or, lightly oil dough, place in a resealable bag, and store in the refrigerator for up to 1 day.
When ready to make the doughnuts, lightly flour your work surface and roll dough to ¼-inch thick. Cut dough into desired size doughnut with cookie or doughnut cutters. For a filled doughnut, do not cut out a center. If using the make ahead dough method, let dough come to room temperature before rolling and cutting.
Place cut dough on prepared baking sheet lined with parchment paper and flour. Allow doughnuts to rise at room temperature for 1 hour.
Pour 2 quarts of oil in a large heavy bottom pot or Dutch oven fitted with a deep fry thermometer and place on medium-high heat. Once oil reaches 360°F on the deep fry thermometer, place several doughnuts in oil and fry 2 minutes per side. Use chopsticks to gently flip the doughnuts over and fry for 1 to 2 minutes on the other side. Transfer fried doughnuts to paper towel lined sheets.
FILLING & TOPPING:
Once the doughnuts have cooled a bit, poke a hole either in the side or on top and fill with jelly, Chocolate Pastry Cream or Lemon Pastry Cream. Sprinkle with powdered sugar or dip in Luscious Vanilla Bean Glaze or Bittersweet Chocolate Glaze.
You could serve Classic Sufganiyot, or you could take your Chanukah OOT (over the top) with this doughnut. Tart lemon curd filling and sweet meringue topping make these doughnuts into mini pies.
Since this filling and topping take about 30 minutes to make, you can start making them while the Classic Sufganiyot are rising before frying.
LEMON CURD FILLING:
Whisk zest and juice, sugar, butter, eggs, vanilla, and salt together in a stainless steel or other non-reactive saucepan over low heat. Continue whisking until curd is thick and starts to bubble.
Place a piece of parchment paper on top of the cream (so that it touches the cream) to cover the surface and keep a skin from forming. Cool completely.
Fill a pastry bag, fitted with a round tip, with lemon curd. Poke a hole in the side or on top of the Sufganiyot and fill.
LEMON MERINGUE TOPPING:
In a medium-size, heatproof bowl, whisk together egg whites and sugar.
Place the bowl over a small saucepan of simmering water, making sure the water doesn't touch the bowl.
Keep whisking the mixture until the sugar has dissolved. You can easily check whether the sugar has dissolved by rubbing a bit of the mixture between your fingers; the mixture shouldn't feel grainy.
Using a stand or hand mixer, beat the warm mixture until the meringue holds a stiff peak and has cooled to room temperature.
Dollop the meringue on top of the doughnuts in “peaks.” Use a kitchen torch to brown meringue for a bruléed effect, or skip the torch and eat.