Trim pork butt of all excess fat leaving 1/4-inch of the fat cap attached.
Combine 2 Tbsp Pork & Poultry Rub, apple juice, brown sugar and salt in a small bowl stirring until most of the sugar and salt are dissolved. Using a meat injector, inject the pork butt every square inch or so with the apple juice mixture. Season the exterior of the pork butt with remaining rub.
When ready to cook, start the Traeger according to grill instructions. Set the temperature to 250 degrees F and preheat, lid closed, for 10 to 15 minutes.
Place pork butt directly on the grill grate and cook for about 6 hours or until the internal temperature reaches 160 degrees F.
Wrap the pork butt in a double layer of foil and pour 1/2 cup of apple juice into the pack. Secure tin foil tightly to contain the apple juice.
Increase grill temperature to 275 degrees F and return to grill in a pan large enough to hold the pork butt in case of leaks. Cook an additional 3 hours or until internal temperature reaches 205 degrees F.
Remove from the grill and discard the bone. Shred the pork removing any excess fat or tendons. Season with additional Pork & Poultry Rub and salt if needed. Combine with Traeger Sweet & Heat BBQ sauce and set aside.
Increase the grill temperature to 450 degrees F and preheat, with the lid closed for 10 minutes.
When grill is hot, place tortillas directly on the grill grate and cook 5-10 minutes or until crispy. Remove from grill and set aside.
Heat olive oil in a medium sauté pan over medium heat. Add bell pepper and onion and cook 5-10 minutes until softened and onion is translucent. Add garlic and sauté 1 minute more.
Add black beans, chicken stock, cumin, chili powder, salt and pepper and bring to a simmer. Cook until liquid is reduced by half, remove from heat and set aside.
Heat 1 Tbsp butter or oil in a non stick pan and cook eggs to desired doneness.
To build, place one tortilla on the plate, top with pulled pork, beans and cheddar. Repeat this pattern, top with egg, hot sauce, and finish with cilantro and lime wedges. Enjoy!
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