In a large mixing bowl, combine the warm water, yeast, and sugar. Set aside for 5 minutes to proof the yeast. Add the eggs, oil, flour, and salt. Mix until combined and then knead by hand for 2-3 minutes. The dough should be a little sticky. If it’s too sticky to knead, add a little more flour.
Cover the bowl and rise for 1 hour, until the dough is double in size.
Preheat oven to 350°F. and line a baking sheet or loaf pan with parchment paper.
Mix the pumpkin puree, brown sugar, cinnamon, cloves, nutmeg, salt and pudding powder together in a small bowl.
Roll out the dough into a large rectangle. Spread the filling all over the dough, leaving about an inch bare around the border.
Roll up the dough into a log and cut the log in half so you have two shorter logs of dough.
At this point, you have so many different ways to shape your babka. The most classic is to twist the dough logs around each other. Slice the tops of the dough lengthwise to expose the inside of the dough. Place in the loaf pan, brush with egg wash and bake.
To make the design in this post, transfer the two logs of dough to the baking sheet. With clean scissors, cut a notch at the start of one dough log at an angle and pull the snipped part out to one side. Cut again and pull the cut part out to the other side. Continue all the way down both dough rolls so that the pieces lie alternately on each side. Cover and let them rise for about 30 minutes.
Brush the dough with egg wash and sprinkle with the cinnamon sugar mixture. Bake for 25-30 minutes, until the crust is golden.
Serve.