In a small bowl, thoroughly combine the butter and flour and set aside.
Encircle each pork shank with butcher's string and tie a tight knot to hold the meat together as it braises. Season generously with salt and pepper.
Heat a Dutch oven over medium-high heat on the stovetop. Add the oil and heat until shimmering. Brown the pork shanks on both sides, working in two batches. With tongs, transfer the shanks to a plate.
Add the carrots, onion, mushrooms, and garlic to the Dutch oven and saut for 5 to 8 minutes.
Add the beer, beef broth, and Worcestershire sauce and bring to a boil over high heat. Reduce the heat, and simmer until the liquid is reduced by one-third. Stir in the tomato paste, and add the chili powder, coffee, bay leaves, and thyme.
Return the pork shanks to the pan and spoon the sauce over them. Cover with the lid.
When ready to cook, start the Traeger grill on Smoke with the lid open until the fire is established (4 to 5 minutes). Set the temperature to 300F and preheat, lid closed, for 10 to 15 minutes.
Transfer the Dutch oven with the pork shanks to the grill grate. Cook for 3 hours, or until the pork shanks are tender.
Add the flour/butter mixture the last 30 minutes to thicken the gravy.
Remove the bay leaves and thyme sprigs from the pot. Transfer the pork shanks to a platter or plates.
Ladle the gravy over the meat, then sprinkle with the parsley. Remove the strings before eating.