Season pork with salt & pepper on all sides and set aside for 10 min. Whisk together remaining marinade ingredients in a small bowl. Reserve 3 Tbsp. marinade for basting. Pour the rest into a zip top bag, add pork, seal and shake lightly to coat. Refrigerate for at least 30 min.
Meanwhile, roast tomatillos, shallot and apple in broiler until blistered and slightly blackened, 8 to 10 min., turning once. In a small bowl, mix Mole Verde Spice, ¼ cup apple juice, 2 Tbsp. olive oil, lime juice and salt into a smooth paste. In food processor or blender, pulse mole paste, roasted ingredients and ¼ cup apple juice until thoroughly blended. Set aside.
Preheat oven to 400 degrees. Heat 1 Tbsp. olive oil in a large saute pan over medium-high heat, add pork and sear all sides until brown, 2 to 3 min. per side. Transfer to an uncovered baking dish and place in oven for 17 min. to cook to medium. Baste twice during cooking with reserved marinade. Remove from oven and let rest for 10 min. before slicing.
Over medium-high heat, add carrots to same large saute pan and cook 2 to 3 min. Add apple cider vinegar and deglaze the pan, scraping up any browned bits with a wooden spoon and reducing liquid by half. Add mole sauce, coat carrots and cook 2 to 3 min., stirring. Stir in stock and remaining apple juice, bring to a boil. Reduce to simmer, cover and cook for 5 to 6 min.
In a separate pan, dry roast pecans until aromatic and lightly browned.
Serve with rice sprinkled with pecans.