Pour ¼ cup warm (105-110F) water in a small bowl. Add yeast to the warm water and let stand 5 minutes. After 5 minutes, stir to dissolve.
Pour yeast mixture into the bowl of a stand mixer. Add remaining (¾ cup) water, honey, eggs, egg yolks, and oil. Whisk to combine.
Place the bowl on the mixer and affix the paddle attachment. On low speed, gradually add half the flour and the salt. Once combined, gradually add the remaining flour. The dough will the soft and rough, and will clean the sides of the bowl as it mixes.
Replace the paddle attachment with the dough hook. On medium-low speed, knead the dough until it is smooth and elastic (about 6 minutes).
turn the dough out onto a lightly floured surface. Knead slightly to ensure it is smooth. Dough should be slightly sticky. If too sticky to work with, you can knead in a small amount of flour.
Grease a large bowl. Shape the dough into a ball. Place dough smooth side down in the bowl, coating it in oil, then turn the smooth side up. Cover the bowl with plastic wrap or a kitchen towel. Let stand in a warm place until doubled in volume, about 1 ½ hours.
Turn the dough out onto an *unfloured* work surface, taking care not to deflate the dough (do not knead the dough). Gently cut the dough into 6 equal pieces (see note).
On a clean work surface (even a tiny bit of flour will make the dough difficult to roll), shape each piece of dough into a rope about 13 inches long.
Line two half-sheet pans with parchment paper or silpats (see note). Line three dough ropes next to each other. Loosely braid the ropes without stretching them. Starting in the center, braid the ropes to the end and tuck the ends under. Turn the loaf around and complete braiding on the other half, again starting in the center and then tucking the ends under.Repeat with the remaining three dough ropes on the second pan.
Cover each braided loaf with a kitchen towel. In a warm place, let rise until doubled in size, about 1 hour.
Position oven racks in the center and top third of your oven and preheat to 375F.
Once the dough has risen, brush the top of each braid with the beaten egg.
Bake for 15 minutes. Switch the position of the breads from top to bottom and front to back. Reduce the oven temperature to 350F and continue baking until the loaves are golden and the bread sounds hollow when tapped with your knuckles, about 50 minutes. If the loaves seem to be browning too deeply, cover them loosely with aluminum foil. Transfer the loaves to a wire rack and cool completely.Enjoy!
Notes
Note on dividing dough evenly: A kitchen scale is handy in ensuring that your pieces of dough are equal in size, which leads to an even braid and even baking. If you don't have a kitchen scale, you can find one here.Note on silpat: I like baking my challah on a silpat because is slows the browning of the bottoms of the loaves, and helps in quick cleanup. If you're interested in purchasing a few for yourself, you can find them here.