Make the dough. In a small bowl, mix 3 tbs of flour and yeast and water. Let sit for about 10 minutes till foamy. In a stand mixer combine the remaining ingredients, add the yeast mixture and mix until the dough is smooth for about 8 minutes. It will be very sticky. Dump the dough on a floured surface and knead with your hands for a couple minutes adding a little bit of flour to make it firmer. Transfer the dough in a large container, seal with plastic wrap, and rise for about 3 hours.
Make ahead. Instead of letting the dough rise, you can place it in a plastic bag and refrigerate for up to 4 days. Pull it out of the fridge and let it stand for 3-4 hours in room temperature before proceeding to the next step.
Make pastry cream right after the you mix the dough to give it enough time for cooling down.
Shape the braid. Line a heavy baking sheet with parchment. Roll the dough on a floured surface into a rectangle about 13x16 inches and about 1/8 inch thick. Apply the chilled pastry cream over the dough and sprinkle with chocolate chips. Roll it into a 16-inch cylinder. Transfer to the baking sheet. Cut the cylinder in half lengthwise and arrange both halves parallel to one another with a cut side facing up. Wrap them around each other starting in the middle, pinching the edges of the braid together. Cover loosely with plastic wrap and let stand at room temperature for another 35-45 minutes.
Bake. Preheat the oven to 350⁰F/175⁰C. Position the rack in the center of the oven. Brush the egg over the braid. Bake until golden brown for about 40 minutes. Let cool on a rack for 1 hour before slicing.