In the bowl of a stand mixer fitted with a dough hook (or a large mixing bowl) combine the water, yeast, and sugar, but do not stir. Let stand for 10 minutes until bubbly.
In a medium bowl, whisk together the flour with the salt. Set aside.
In a small bowl, whisk together the eggs, honey, oil, and vanilla.
Once the yeast mixture is ready, add in both the flour mixture and the egg mixture. Use a rubber spatula to begin to combine. If using a stand mixer, turn the mixer on and knead until the dough pulls away from the sides and is tacky. If the dough is still very sticky, add more flour a little at a time. If not using a stand mixer, knead on a lightly floured surface. Shape into a ball.
Temporarily remove the dough from the bowl, spray the bowl with cooking spray and put the dough back in the bowl. Cover the bowl with plastic wrap and let rise in a warm place for 90 minutes - 2 hours, or until doubled in size. While the dough is proofing, make the filling.
Pumpkin Pie Filling
Preheat oven to 400 degrees. Spray a 9x9" baking dish with cooking spray. Set aside.
In a large mixing bowl, whisk together the sugar, brown sugar, cornstarch, spices, and salt. Add in the pumpkin, cream/oat milk, sour cream, and 1 egg.
In a small bowl, beat the remaining egg. Add in half of the egg into the batter, and reserve the other half. (You'll use this to egg wash the loaf later)
Pour the mixture into the prepared pan and bake for 50 minutes until set. Set aside to cool.
Roll out the dough into a rectangle on a lightly floured surface. Spread the pumpkin pie filling leaving a small border of dough. Roll the dough into a log from the long side (resulting in a long log). Use a sharp knife to cut the log lengthwise (2 long halves). Pinch the top of the 2 logs together and braid them together, over/under.
Spray a loaf pan with cooking spray. Tuck the ends of the loaf under themselves so the loaf fits in the pan, and place the loaf in the pan. Cover the pan with plastic wrap and let rise for 45 minutes.
Preheat oven to 375 degrees. Take the leftover egg and mix it with 1/2 a tsp of milk/oat milk. Brush the egg wash onto the loaf and bake for approximately 35 minutes. I recommend checking the doneness with a thermometer, 190 degrees and you're good to go! If the loaf is browning more than you like, loosely cover the loaf with aluminum foil.
Remove from oven and allow to cool completely. While the loaf is cooling, prepare the glaze.
Whisk the confectioner's sugar, vanilla extract, and cream/oat milk together until smooth. Drizzle over the cooled loaf and enjoy!
Pumpkin Pie Babka https://500spatulas.com/pumpkin-pie-babka-baking-with-yeast/