1. Prepare dough for soofganiyot and let it rise.

2. Lightly coat a large tray with flour. Roll out half the dough on a floured surface until it is ¼-inch thick, flouring dough occasionally. With a 2½- to 3-inch cutter or a glass of similar diameter, cut dough into rounds. Put 1 teaspoon apricot or strawberry preserves on the center of half the number of rounds. Brush the rim of one round lightly with water. Set a plain round on top. With floured fingers, press edges of round firmly all around to seal it. Transfer this “sandwich” immediately to tray. If it has stretched out to an oval, plump it gently back into a round shape. Continue with remaining rounds and remaining dough, placing each ½ inch apart on the tray. Cover them with a damp cloth and let rise in a warm place about 30 minutes.

3. Knead the scraps of dough, put them in an oiled bowl, cover with a damp cloth, and let rise about 30 minutes.

4. Line a tray with paper towels. Pour oil into a deep fryer or deep, heavy saucepan. Do not fill pan more than halfway with oil. Heat oil to 350°F; if a deep-fat thermometer is not available, test by adding a small piece of dough to oil; oil is hot enough when it bubbles gently around dough. Add 4 doughnuts; do not crowd them. Fry doughnuts about 3 minutes on each side or until golden brown. If they brown too quickly, reduce heat so they have a chance to cook through. Drain on paper towels. Pat the tops gently with paper towels to absorb excess oil.

5. If you like, make more doughnuts with the scraps; they won’t be as light but will still be good.

6. Put soofganiyot on a serving dish and sift powdered sugar over them. Serve warm or at room temperature. Do not serve these immediately because the jam is boiling hot.