Preheat the oven to 375°F. Line a baking sheet with foil. Wrap each sweet potato in a piece of foil and place it on the baking sheet.
Bake on center rack of the oven for 45 minutes to 1 hour and 15 minutes, or until potatoes are soft to the touch and a knife can easily pierce through the flesh. Time will vary depending on the size. You can also start to smell the sweet aroma as it gets closer to being fully cooked.
Season both sides of the chicken breasts with salt, pepper, and paprika. Heat a large frying pan or cast iron skillet over medium-high heat. Add 1 tablespoon of oil and allow it to heat up.
Carefully add the chicken and allow it to cook for 6 minutes. Flip to the other side, reduce heat to medium and cook another 6 to 7 minutes, or until no longer pink and the internal temperature of the chicken reaches 165°F.
Transfer to a clean plate to allow to rest and cool slightly. Once slightly cooled, chop the chicken into ½ inch cubes.
In the same pan as you cooked the chicken keep the heat at medium. Add the garlic and shallot, cook for about 1 minute until fragrant, stirring continuously. Add the bell pepper and cook 2 minutes, stirring as needed. Add the kale and spinach and cook until just wilted, about 2 minutes and stirring continuously. Lightly season with salt and pepper to taste. Turn off heat and set aside.
Once sweet potatoes are finished cooking, unwrap. Make cuts ¾ of the way through the center of the potato to allow for stuffing. Use a fork to fluff up some of the sweet potatoes so it looks mashed.
Evenly divide the sauteed vegetables and add them into each sweet potato. Top with equal amounts of diced chicken. Drizzle the top with warmed barbecue sauce as desired. Garnish with green onions and cilantro.