In a large bowl or plastic container with a lid, combine the cocoa, cornstarch, sugar, dry milk, and salt. Store in an airtight container in the refrigerator for up to 3 months.
Place 1 3/4 cups of dry pudding mix into a medium saucepan. Add the milk and heavy cream, and whisk to combine. Over medium heat, bring mixture to a boil, continuously whisking gently. Reduce heat to low and cook for 4 minutes while continuing to whisk. Remove from heat and stir in vanilla. Pour the mixture through a sieve and into individual dishes or a 1 1/2-quart serving dish. Cover the surface of the pudding with plastic wrap. Place in the refrigerator to chill completely before serving, approximately 4 hours.