Separate 1 large egg, saving the white. Mix the yolk with 2 large eggs, ¾ cup of lukewarm water, 6 tablespoons of vegetable oil, and 3 tablespoons of honey.
Add 4 cups of unbleached all-purpose flour, 1½ teaspoons of salt, and 4 teaspoons of instant yeast. Knead until soft and smooth, then cover and let rise for about 2 hours.
Divide into 3 pieces and roll each into a 20in / 50cm rope, resting the dough for 10 minutes if it springs back. Braid the ropes, tuck the ends under, and place on a parchment-lined baking sheet.
Cover and let rise for 60-90 minutes, until very puffy. Toward the end, preheat the oven to 375°F / 190°C with a rack in the upper third.
Whisk the reserved egg white with 1 tablespoon of cold water and brush over the loaf. Bake for 25-30 minutes, until deep golden and a thermometer in the center reads 190°F / 88°C.
