Sponge:
Combine water, yeast, and flour in the bowl of a stand mixer. Cover with a towel and let stand for 30 minutes, until the surface looks like a sponge.
Dough:
To the sponge add oil, honey, egg yolks, whole eggs, and flour and mix to combine.
Add flour, a little at a time until dough is not sticky, but still has a bit of tackiness to it.
Transfer dough to a lightly greased bowl. Cover and rise for 2 hours. Or lightly oil the dough and transfer to a resealable bag and store overnight in the refrigerator (see note under photo).
Chocolate Filling:
In a medium bowl, stir together chocolate, sugar, cinnamon, and salt together. Set aside.
Pumpkin Filling:
In a medium bowl, stir together pumpkin, sugar, cinnamon, cloves, nutmeg and salt together. Set aside.
Shaping and Filling:
Lightly grease 3 loaf pans with oil. Separate risen dough into 3 equal pieces. If using refrigerated dough, let it come to room temperature before shaping.
With a rolling pin, roll one piece of dough into a 16-inch square. Sprinkle 1/3rd chocolate filling on half of the square. Shmear the other half with 1/3 of pumpkin filling. Roll dough up tightly into a rope, being sure to seal the ends.
Slice rope lengthwise and wrap the halves around each other at least 6 times. Fold rope in half and place in a greased loaf pan. Repeat with remaining dough. Allow babkas to rise for 1 hour.
Preheat oven to 350°F.
Bake babkas at 350°F for 40 minutes, rotating the pans halfway through. Remove from the oven and cool in the pan on a rack for 10 minutes. Remove babkas from the pans and cool on the rack for 10 minutes more. Drizzle with cinnamon glaze, slice, and serve warm.
Cinnamon Glaze:
Whisk together sugar, water, cinnamon, and salt. Drizzle over cooled babkas.