1. Place the flour, sugar, and salt in the work bowl of a food processor fitted with a metal blade. Pulse until mixed.

2. Place the water in a mixing bowl and whisk in the yeast. Whisk in the oil, eggs, and yolk.

3. Add the liquid to the work bowl and pulse 8 or 10 times until the dough forms a ball. Let rest for 5 minutes, then run the machine continuously for 30 seconds.

4. Turn the dough out onto a floured work surface (you may need the help of a scraper). Knead the dough lightly to form a ball. Invert into an oiled bowl and turn the dough to coat all sides with oil. Cover the bowl with plastic wrap and allow the dough to rise at room temperature until the dough has doubled, about 1 hour.

5. Turn the risen dough out onto a floured work surface and press the dough with the palms of your hands to deflate. Divide the dough into three equal pieces. Roll each piece into a cylinder, 12 to 15 inches long. Arrange the strands side by side on the prepared pan. Begin to braid in the middle of the strands and braid to one end. Turn the pan around and braid from the middle to the other end. (Braiding from the middle outward helps keep the loaf a consistent width.) Pinch each end to seal the strands together and turn the pinched parts under the loaf. Cover with oiled plastic wrap and allow to rise at room temperature until the dough has doubled, about 1 hour.

6. When the loaf is almost doubled, set a rack at the middle level of the oven and preheat to 400 degrees.

7. Brush the top and sides of the risen loaf with the egg wash. Bake for 20 to 25 minutes, or until the top is golden brown and the internal temperature of the loaf reaches about 210 degrees.

8. Transfer to a rack to cool.