Step 1

In a large bowl, stir together the warm water and yeast. Let stand until foamy, about 5 minutes. Add 3/4 cup flour, 1/4 cup sugar, and salt; mix until well combined. Add egg yolks and remaining 1 3/4 cups flour. Mix until combined, then knead dough in bowl until all flour is incorporated. Turn out dough onto a lightly floured work surface; knead a few minutes until smooth. Knead in margarine until incorporated.

Step 2

Transfer dough to a well-oiled bowl, turning several times to coat entirely with oil. Cover tightly with plastic wrap, and refrigerate overnight.

Step 3

Bring dough to room temperature, about 30 minutes. On a lightly floured work surface, roll out dough into an 11-inch square, about 1/8 inch thick. Using a 2-inch cookie cutter (or a glass), cut out about 24 (2-inch) rounds, dipping cutter in flour as needed to prevent sticking. Reroll scraps; cut out about 16 more rounds.

Step 4

Line a baking sheet with a clean kitchen towel. In a small bowl, lightly beat egg whites. Brush edge of a dough round with egg white, then mound 1/2 teaspoon jam in center. Top with another round; press edges to seal. Repeat with remaining rounds. Transfer to prepared baking sheet; let rise until puffy, 20 to 30 minutes.

Step 5

Heat a few inches of oil in a large, heavy pot until it reaches 360 degrees on a deep-fry thermometer or a scrap of dough sizzles upon contact. Working in batches of 4 or 5, carefully slip doughnuts into hot oil. Fry, turning once, until golden brown, about 1 minute (doughnuts will fry very quickly and puff up). Using a slotted spoon, transfer doughnuts to paper towels to drain.

Step 6

Place remaining 1/2 cup sugar in a medium bowl.While doughnuts are still hot, dip them in sugar, turning to coat. Serve immediately.