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Place sugar, cornstarch, and salt in a heavy-bottomed saucepan. Place over medium-low heat. Slowly add whole milk, a little at a time, whisking constantly to keep lumps from forming. Continue to add all of the milk.
Cook for 10-12 minutes, stirring often, until the mixture is thick enough to cover a back of a spoon.
Add the chocolate chunks, a little at a time, whisking often. Cook for 3-4 minutes or until chocolate is melted and the mixture is thickened.
Stir in vanilla extract. Pour it into a bowl and place Saran Wrap directly over the pudding to keep it from forming a skin. Let chill for 2-3 hours. To expedite the process, place the bowl in an ice-water bath.
Serve chilled with freshly sweetened whipped cream and chocolate shavings.
Nutrition information is automatically calculated, so should only be used as an approximation.
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