Roast the sweet potatoes. Preheat the oven to 425°F. Toss the sweet potato cubes with olive oil, salt, pepper, and smoked paprika, then spread them in a single layer on the sheet pan with space between pieces — crowding them is what causes steaming instead of roasting. Roast for 22–25 minutes, flipping once halfway, until the edges are deeply browned and a fork slides in with just a little resistance.
Cook the chicken. While the sweet potatoes roast, season the chicken with salt, garlic powder, and onion powder. Cook in a skillet with the olive oil over medium heat, about 6–7 minutes per side for breasts (less for thinner cuts), until it reaches 165°F internally. Alternatively, poach it in simmering water for about 12 minutes if you’d rather not stand over a skillet.
Shred the chicken while it’s still warm. Let the chicken rest for 5 minutes, then shred it with two forks or in a stand mixer on low speed. Shredding warm chicken pulls apart more easily and absorbs the sauce better than chicken that’s gone cold and firmed back up.
Build the sauce, and finish it off the heat. Warm the BBQ sauce in a small saucepan just until it loosens slightly, then remove it from the heat entirely before stirring in the apple cider vinegar and smoked paprika. This is the one step worth not skipping: simmering vinegar for even a minute or two cooks off the sharpness that makes BBQ sauce taste bright instead of just sweet, so adding it after the heat is off is what keeps the sauce from tasting flat and syrupy.
Toss the chicken in the sauce. Add the shredded chicken to the sauce and toss until every piece is coated. Taste and add a touch more vinegar if it still leans too sweet for you.
Assemble the bowls. Divide the lettuce or spinach among four bowls, then top with roasted sweet potato, BBQ chicken, corn, red onion, and cilantro.
