In a mixer, with a dough hook attachment, add the warm water, yeast and a teaspoon of sugar. Mix until blended. Let the yeast bloom (could take up to 5 minutes). Once it has bloomed, slowly mix in 1 cup of the flour until combined.
Mix in the eggs one at a time until they are combined. Add in the rest of the sugar and the oil. Mix until combined.
Add in the sourdough discard.
Slowly add the rest of the flour (and the salt) with the mixer on medium-low speed, and mix until combined. Stop the machine as you add each cup of the flour to scrape the sides of the bowl and incorporate the flour.
Mix on low speed for 12 minutes until dough is incorporated. Be sure to give your mixer a break and as you don’t want to burn it out. Add flour, if needed, 1 tablespoon at a time. The dough will be a little sticky but also firm.
Take dough out of mixer bowl, and place it on a clean counter or work space. Knead the dough a minute or so on the counter. Check the dough and if it is still too sticky to work with, add a tablespoon of flour to make it pliable.
Form the dough into a ball and place into an oiled bowl (when I put the dough in the bowl I swish the dough around the bottom of the bowl and then flip it over so all of the dough is covered in a light film of oil). Cover with plastic wrap and let it rise at room temperature until doubled in size (about 1-1 1/2 hours).
When the dough has risen, punch down the dough. Divide the dough into 6 equal portions. Shape each portion into a ball, and allow it to rest with plastic wrap on it for 5-10 minutes.
Use your hands to roll each dough ball into a long piece. Pinch the seams of the first 3 strands and braid together to form a loaf. Tuck the ends of the strands under on both ends nice and tightly. Place the braided bread on a parchment lined baking sheet.
Repeat the process with the other 3 strands of dough.
Cover with plastic wrap and let rise in a draft free place for about 45 minutes to 1 hour.
Preheat oven to 350 F.
When ready to bake, brush with egg wash (egg wash is the egg and sugar whisked together in a small bowl).
Bake the challah for 35-40 minutes. The bread should be golden brown. Ovens may vary so check your challah at about 30 minutes and see how it’s doing. You test if it’s done by tapping the bottom of the loaf. If it sounds hollow, it needs a bit more time.* Be careful to not burn your fingers like I did when you do that test. Let it cool and serve slightly warm or at room temperature.