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