Combine lukewarm water, yeast, and 1 teaspoon of sugar in a small bowl.

Let stand for 10 minutes until foamy.

In a large mixing bowl, add flour.

Create a well in the center.

Add remaining sugar, eggs, yolks, butter, vanilla, lemon rind, remaining water, and salt to the well.

Mix the wet ingredients in the well.

Add the yeast mixture to the well.

Mix all ingredients until a dough forms.

Knead the dough with a dough hook for 5 minutes on medium speed.

If sticky, add 2 tablespoons of flour.

Continue kneading for 5 minutes until smooth.

Place the dough in an oiled bowl and coat all sides.

Cover with a damp cloth and let rise in a warm place for 1 to 1.5 hours, or until doubled in size.

Lightly flour a large tray.

Roll out half the dough on a floured surface to 1/2-inch thickness.

Cut out rounds using a 2.5 to 3-inch cutter.

Transfer rounds to the prepared tray, spacing them 1/2-inch apart.

Repeat with remaining dough.

Cover the rounds with a damp cloth and let rise for about 30 minutes.

Knead the scraps of dough, place in an oiled bowl, cover, and let rise for 30 minutes.

Line a tray with paper towels.

Pour oil into a deep fryer or saucepan, no more than halfway.

Heat oil to 350°F.

Test the oil's heat with a small piece of dough; it's ready when it bubbles gently.

Add 4 or 5 doughnuts to the oil at a time.

Fry for about 3 minutes per side, until golden brown.

Adjust heat if browning too quickly.

Drain on paper towels.

Pat the tops with paper towels to remove excess oil.

If desired, make more doughnuts with the scraps.

Place doughnuts on a serving dish and dust with powdered sugar.

Serve hot, warm, or at room temperature.