In a medium bowl, combine water, instant yeast, honey, pumpkin puree, oil, 1 egg, and egg yolk.
In the bowl of a stand mixer fitted with a dough hook, add flours, pumpkin pie spice, and salt. Stir until combined.
Remove the hook. With your hands, make a well in the center of the flour mixture. Pour wet ingredients into the hole. Attach the hook and turn mixer on low to combine the ingredients until a ball forms.
Once a ball has formed, remove from the bowl and onto a floured surface to knead by hand for 10 minutes. Or you can continue to knead in your stand mixer for 5 minutes. I like kneading by hand because it's sort of therapeutic. And quite the workout! You'll know it's done with it's much softer, smoother, and elastic.
Grab a large bowl and grease it lightly with cooking spray or vegetable oil. Shape dough into a ball and place into greased bowl. Cover top of bowl with a damp paper towel and place in draft-free place to proof for 1 1/2 hours. I always place dough in my microwave to proof and it works like a charm.
Once it's proofed for 1 1/2 hours, punch dough down with your fist and remove from bowl and onto floured surface. Cut dough into three even pieces.
Now we're going to braid the dough. Roll each piece of dough into a long, 14-inch log. Braid the dough and tuck the ends under. If you haven't braided dough before, I used an awesome tutorial on how to braid your challah. I included a link to the tutorial in the notes below.
Place a sheet of parchment paper on a baking sheet. Add challah to the baking sheet. Cover loaf with a towel and let it rise for 45 minutes until it's about double in size.
When there's about 20 minutes left for the dough to rise, preheat the oven to 350 degrees.
Once the dough has risen, whisk the water and egg for the egg wash. With a pastry brush, brush two coats of egg wash all over the loaf. Make sure to get the sides too!
Bake loaf in a preheated oven until it is golden brown all over, about 35-40 minutes. Make sure to rotate the loaf 180 degrees halfway through baking so that it bakes evenly.
Once it's done, remove from the oven and let it cool completely before slicing so that you get smooth, even slices.