Mix flour, sugar, yeast, and salt in the bowl of a stand mixer fitted with the dough hook on low speed to combine, about 1 minute. With the mixer running, pour in the water and the egg, mixing well after each addition. Continue mixing, scraping down the sides of the bowl as needed, until the dough is cohesive but still a bit sticky, about 3 minutes. Add the margarine and mix to fully incorporate it into the dough. Increase the speed to medium and mix until the dough is smooth and elastic, 7-9 minutes. Cover the dough with plastic wrap or a clean kitchen towel. Set the dough in a warm place and let rise until doubled in size, about 1 hour.
Cut 18 (3- to 4-inch) squares of parchment paper and place on a clean work surface. Once the dough has risen, lightly oil your hands and pinch off 18 balls (each should weigh about 65 grams). Place each ball on a parchment square. Cover the dough balls with a clean kitchen towel and let rise for 25 minutes, until puffy and almost doubled in size.
While the doughnuts are rising, line 2 sheet pans with paper towels. Fill a medium or large heavy bottom pot, such as a Dutch oven, with 2 inches of oil. Heat the oil over medium until it reaches 365F.
Fry the doughnuts: Working in batches of 2 or 3 doughnuts at a time (depending on whether your pot is medium or large), carefully drop the doughnuts on the parchment paper into oil. The parchment will slide off immediately: carefully remove it with a spider or tongs. Adjusting the heat as needed to maintain oil temperature, fry the doughnuts until puffed and golden brown, flipping with a spider or slotted spatula, about 2 minutes per side. Remove the doughnuts to the prepared sheet pans and let cool completely.
Use a chopstick or the handle of a wooden spoon to poke a hole (but not all the way through) on the side of each doughnut. Fill a piping bag with the jam or chocolate spread, then fill each doughnut. Place doughnuts on a wire rack placed over a sheet pan and dust with powdered sugar. Serve immediately. Sufganiyot can be stored in an airtight container in the refrigerator 2-3 days.
