In a large saucepan, whisk together the sugar, cornstarch, cocoa powder, and salt until well combined. Whisk in the milk, making sure to get all the dry bits incorporated.
Heat the mixture over medium-high heat, stirring constantly until it thickens and starts to bubble lightly, about 6 to 8 minutes.
Remove from heat. Stir in the chocolate chips and vanilla extract.
Divide the pudding into six 4-ounce ramekins. Place a bit of plastic wrap or waxed paper ON the surface of the pudding to prevent a skin from developing.
Refrigerate for several hours until cold. Serve with whipped cream if desired.
Promptly store leftovers in an airtight container in the refrigerator, for up to 3 days.Nutritional values are approximate and based on 1 serving.Flavor variations: for a different flavor, stir in 1/4 teaspoon of another extract, such as coffee, almond, or peppermint. For mocha flavored pudding, add a tablespoon of instant coffee powder to the dry mixture.