When ready to cook, start the Traeger grill on Smoke with the lid open until the fire is established (4 to 5 minutes).
Combine 1-1/4 cup milk, 1/4 cup sugar and the salt in a shallow baking pan and place directly on the grill grate. Smoke for 35 to 40 minutes or until the milk has picked up desired amount of smoke flavor. Transfer milk and sugar mixture to a small sauce pan and bring to a boil over medium heat.
Meanwhile, in a medium bowl whisk together the cornstarch, cocoa powder and remaining sugar. Whisk in remaining milk until smooth. Add mixture to hot milk in the saucepan and bring to a boil over medium heat, whisking constantly, until the pudding is thick enough to coat the back of a spoon.
In another medium bowl, whisk the whole egg with the yolks. Gradually whisk about 1 cup of the hot milk into the eggs until fully incorporated and the temperature of the eggs matches that of the milk. Add this mixture back to the sauce pan and whisk to combine.
Cook over medium heat whisking constantly just until it comes to a boil. Add chopped chocolate to a medium heatproof bowl.
Strain the pudding into the bowl with the chocolate through a fine mesh strainer. Add butter and vanilla and whisk until the chocolate and butter are incorporated and pudding is smooth.
Transfer to serving dishes and refrigerate until well chilled. Enjoy!
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