Make the sponge: In the bowl of a stand mixer, stir together water, flour, yeast, and salt. Cover; let mixture sit in a warm place for at least 30 minutes and up to 2 hours. The surface should look bubbly and like a sponge.
Fit stand mixer with a dough hook attachment. With mixer on low speed, add sugar, oil, vanilla extract, eggs and yolks.
Add remaining flour, 1/2 cup at a time and knead until the dough is smooth and tacky, but not too wet or sticky.
Cover and allow dough to rest for 1 hour in a warm place, or until it doubles in size. Alternatively, you can cover and allow it to slowly rise in the refrigerator overnight. Assemble Kokosh: Line 2 baking sheets with parchment paper. (You can fit two kokosh cakes lengthwise onto one tray, just keep them a few inches apart.)
Once dough doubles in size, punch down and divide into three equal pieces. (If refrigerated overnight, allow dough to come to room temperature before proceeding.)
Preheat oven to 350°F.
Roll each piece into approximately a 10x14-inch rectangle. Spread 1/3 cup of chocolate spread over each dough.
Make filling: Combine sugar, cocoa, salt and coffee (optional) in a small bowl. Sprinkle 1/2 to 2/3 cup over each dough.
Roll each piece into a log, starting from the shorter side and pinch edges to seal. Use a rolling pin to slightly flatten the kokosh cake. Place on prepared baking sheets.
Brush with egg wash and bake for 20-25 minutes, until light golden brown.