For the bao starter: In a large mixing bowl, combine the flour, water, sugar and yeast. Let stand until puffed up and has bubbles on the surface, about 20 minutes.
For the chocolate sauce: In a medium bowl, mix together the chips, butter and vanilla. Place the bowl over a barely simmering saucepan of water and stir until the chocolate has melted. Whisk in the cream until the mixture is smooth. Set aside to cool to room temperature.
For the chocolate bao: In a large bowl, whisk together both flours, the cocoa powder, sugar, baking powder and salt. Add the flour mixture and oil to the starter and stir together while gradually adding 1/2 cup room temperature water. Stop adding water once the dough has come together enough to knead by hand. Dump the dough onto a lightly-floured surface and knead until you have a smooth, satiny dough, 3 to 4 minutes. Return the dough to the bowl and cover tightly with plastic wrap. Let the dough rise in a warm place until it has doubled in size, about 3 hours.
Spray a stainless-steel steamer with vegetable oil cooking spray. Use your hands to roll the dough into a long log, about 2 inches wide and 12 inches long. Cut the log into 12 equal pieces. Place a few chocolate chips in the center of each dough piece and stretch the dough around the chips, pinching one end to form a ball. Place the ball seam-side down onto a wax paper square. Continue with the remaining pieces of dough.
Gently lower the bao in batches into a prepared steamer. Steam for 10 minutes, then carefully remove and let cool under a kitchen towel.