Preheat the oven to 400 degrees F. Put a piece of aluminum foil on the middle rack. Scrub each sweet potato, and use a fork to poke a few holes in the skin. Place the potatoes on the foil and bake for 35 to 45 minutes, or until soft to the touch.
While the potatoes are baking, combine the ketchup, brown sugar, Worcestershire sauce, apple cider vinegar, and smoked paprika in a small sauce pan. Whisk and cook over medium heat until simmering, stirring occasionally (this will happen quickly). Add the pinto beans to the sauce and mix until they are coated. Heat for another 3 to 5 minutes. Remove from heat and add the barbecue beans to a large bowl.
When the potatoes are finished, slice each one in half down the middle. Scoop out the flesh with a spoon, leaving a ¼" border in each skin. Add the flesh to the bowl with the beans and mix them together. Mix in the sliced scallions and cheese, but be sure to reserve some scallions for serving.
Put the skins on a baking sheet lined with parchment paper or aluminum foil. Stuff each skin with a large spoonful of the filling. Sprinkle with shredded cheese. Pop back in the oven for 10 to 15 minutes or until the cheese is melted and the filling is heated through. Serve warm with lime and a few sliced scallions and cilantro on top. Enjoy!