In a 4 quart sauce pan over medium heat whisk the heavy cream, ¼ cup sugar and vanilla bean paste to combine and bring to a simmer. Place the egg yolks, ¼ cup sugar, cornstarch and cocoa powder in a large heatproof bowl and whisk to incorporate.
Add the chocolate chips to the cream and cook over medium heat until the chocolate has completely melted, whisking frequently to prevent scorching on the bottom. As soon as the chocolate has melted, slowly pour into the egg yolks, whisking constantly to incorporate and prevent the egg yolks from scrambling. Pour the custard back into the pot. Cook over medium heat until thickened, 2 to 3 minutes, whisking constantly.
Remove pan from the heat and gently stir in the butter. Place the pudding in a large glass bowl or 8 ramekins and chill for at least 1 hour or overnight. Serve cold with freshly whipped cream. Pudding will keep for up to to 4 days stored in an airtight container in the refrigerator.