1. Pour ½ cup lukewarm water into a small bowl. Sprinkle yeast on top and add 1 teaspoon sugar. Let stand 10 minutes or until yeast is foamy.
2. Spoon 4 cups flour into the large bowl of an electric mixer fitted with a dough hook. Make a well in center of flour. To the well add remaining sugar, eggs, yolks, butter, vanilla, grated lemon rind, remaining water, and salt. Mix the ingredients in the well until blended. Add yeast mixture. Mix until the ingredients come together to form a dough.
3. Knead with dough hook at medium speed, scraping down the dough occasionally, 5 minutes. If the dough is very sticky, add 2 tablespoons flour. Knead 5 more minutes or until very smooth. Put dough in a clean, oiled bowl and turn to coat it with oil. Cover with a damp cloth and let rise in a warm place 1 to 1½ hours or until doubled in volume.
4. Lightly coat a large tray with flour. Roll out half the dough on a floured surface until it is ½-inch thick, flouring dough occasionally. With a 2½- to 3-inch cutter or a glass of similar diameter, cut dough into rounds. Transfer rounds to tray, placing them ½-inch apart. Continue with remaining dough. Cover rounds with a damp cloth and let rise in a warm place about 30 minutes. Knead the scraps of dough, put them in an oiled bowl, cover with a damp cloth, and let rise for about 30 minutes.
5. 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 or 5 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.
6. If you like, make more doughnuts with the scraps; they won’t be as light but will still be good.
7. Put soofganiyot on a serving dish and sift powdered sugar over them. Serve hot, warm, or at room temperature.