Heat about 2 tablespoons extra-virgin olive oil in a large skillet over medium-high heat. Season pork roast with salt and pepper. When the oil is hot, add the pork roast and sear on all sides. Transfer the pork to a crock pot.
In a small bowl, whisk together the brown sugar, onion, garlic powder, cumin, coriander, oregano, and smoked paprika. Rub it over the top of the pork roast. Whisk together the Coke, adobo sauce, apple cider vinegar, and liquid smoke and pour it around the pork roast.
Cover and cook on low for 8-10 hours or on high for 5-6 hours or until it shreds easily with a fork. Juice the lime over the pork and stir to combine, then season to taste with salt. Serve with lime wedges, crumbled queso fresco, fresh pico de gallo, sliced white onions, chopped cilantro, sliced avocado, and any other favorite taco toppings.