Preheat oven to 375 degrees F. Spray one 9 by 17-inch sheet tray with vegetable spray, line with parchment paper and spray again. In a mixer, using the whip attachment, whip the egg yolks and the sugar until doubled in volume and pale yellow; add vanilla extract. Sift together the flour, cocoa powder, and baking powder and powdered sugar twice. Slowly add the dry ingredients to the mixing bowl, running at slow speed, until fully incorporated.
In a clean and greaseless bowl, whip the egg whites until firm but not dry. Incorporate a fifth of the whipped egg whites into the cocoa mixture and mix until well incorporated. Fold the remaining egg whites into the cocoa mixture in 3 batches and immediately spread onto a large baking sheet using an offset spatula, being careful not to overwork the dough. Bake for 6 to 8 minutes.
Immediately run the tip of a knife around the edge of the cake to loosen it from the sides of the sheet tray then slide it (with the parchment paper) onto a cool surface. Trim dry edges of the cake.
Vanilla Cream Filling: With an electric mixer, beat together the butter and the vegetable shortening until blended. Turn the mixer down to its lowest setting and gradually add the confectioners' sugar. Turn the mixer back up and beat at high speed until light and fluffy, about 5 minutes. Gradually beat in the vanilla and corn syrup until the filling is the consistency of sour cream, about 2 minutes more.
Using a sharp knife, cut the cake in half lengthwise. Using an offset spatula, spread a 1/8-inch thick layer of vanilla cream filling over half of the cake and cut into 5 equal sections per half. Roll up each section tightly (peeling off parchment paper as you roll) and place in the freezer for 30 minutes.
Melt the bittersweet chocolate in the top of a double boiler and add cocoa butter or vegetable oil. Place the rolls 1 at a time directly in the double boiler of melted chocolate. Coat each roll completely in the chocolate. Using two forks, carefully transfer the rolls to a parchment-lined tray, allowing any excess chocolate to drip back into the double boiler. Continue with the remaining rolls, pouring more of the chocolate onto the plate as needed.