Mix together sugar, cornstarch, cocoa powder and salt in a medium sized heavy saucepan, then gradually whisk in milk. Bring the mixture to a boil over moderately high heat, whisking constantly. Continue whisking for 2 minutes until mixture is thick. Remove from heat and whisk in the chocolate and vanilla until smooth.
Transfer to a bowl and cover pudding with a piece of wax paper or plastic wrap so it sticks to the surface (to prevent a skin from forming) and chill in the refrigerator until cold, at least 2 hours.
Makes approximately 2 cups.