In a large, heavy saucepan, whisk the cocoa powder, cornstarch, and cream together to form a smooth mixture. Add the egg yolks, milk, brown sugar and salt and whisk well to combine. Heat over medium-high heat, whisking constantly, until mixture just comes to a simmer. Reduce the heat to low and cook, stirring constantly, until mixture thickens to form a smooth, thick pudding. Remove from the heat and add the chocolate and vanilla extract. Stir until the chocolate has melted into the pudding base and a smooth, thick pudding is formed. Strain mixture through a fine sieve if you see any lumps, then transfer to a clean bowl and cover with plastic wrap, pressing so that the plastic sits directly on top of the pudding. Refrigerate the pudding until thoroughly chilled, several hours or up to overnight.

When you are ready to assemble the cake, whisk to loosen the pudding slightly. Use to fill between the layers of a 3- or 4- layer cake.