Warm the bowl of an electric mixer fitted with the dough hook by rinsing it with hot water. Pour the warm water into the bowl (be sure it's at least 110 degrees F when it?s in the bowl) and mix in the yeast, sugar and saffron. Allow to sit for 5 minutes, until it starts to froth, which tells you that the yeast is active. Add the eggs and egg yolk and mix on low speed. With the mixer on low, gradually add 4 1/2 cups of the flour, scraping down the bowl as you go. With the mixer on low, add the salt and butter, then slowly add between 1 and 1 1/2 more cups of the flour, mixing on low for about 5 minutes and continuing to add a dusting of flour to the bowl but only enough so the dough doesn't stick to the bottom of the bowl. The dough will be soft and a little sticky.
Turn the dough out onto a floured board and knead it by hand for a full 2 minutes. Roll the dough into a ball with the smooth side up. Brush a large bowl with vegetable oil and place the dough in the bowl, smooth-side down. Roll the dough around to cover it with oil, then turn it smooth-side up, making sure the entire dough is covered with oil to prevent a crust from forming. Cover the bowl with a clean dry kitchen towel and allow to rise in a warm place for about 2 hours, until doubled in size.
Punch the dough down lightly and turn it out onto an unfloured cutting board. With a sharp knife, cut the dough into 4 equal pieces. Line a sheet pan with parchment paper. Turn the first ball of dough smooth-side up and roll it into a cylinder. Roll the dough into a rope 17 inches long and lay it seam-side down on the parchment paper. Repeat for the other 3 balls of dough, laying them side by side on the parchment paper.
To braid the dough, pile one end of the ropes on top of each other and pinch them together and under. With the pinched end away from you, take the far right rope and move it left over 2 ropes. Then take the far left rope and move it right over 2 ropes. Continue taking alternate ropes and laying them over 2 ropes until you?ve braided the entire bread. Pinch the ends together and fold them under. Cover the bread with a clean dry kitchen towel and allow it to sit in a warm place for 45 to 60 minutes, until doubled in size.
Meanwhile, preheat the oven to 350 degrees F. Place an oven rack in the lower third of the oven. Brush the bread thoroughly with the egg wash and bake for 35 to 40 minutes, until the outside is browned and it sounds hollow when you tap the bottom. Place the challah on a baking rack and cool completely.
Photograph by Steve Giralt
To make ahead, bake the challah, cool completely, wrap tightly and refrigerate for up to 3 days or freeze for up to 4 months.
Recipe from Cooking For Jeffrey: A Barefoot Contessa Cookbook. Copyright (c) 2016 by Ina Garten. By arrangement with Clarkson Potter/Publishers, A Division of Random House, LLC.