Heat the oven: Preheat to 425°F (220°C). Line a large sheet pan with parchment for easy cleanup.
Season the sweet potatoes: Toss the cubes with olive oil, smoked paprika, garlic powder, onion powder, salt, and pepper.
Spread in an even layer on the sheet pan.
Start roasting: Roast the sweet potatoes for 12 minutes to give them a head start.
Prep the chicken: While the potatoes roast, cut the chicken into bite-size pieces or keep them as whole breasts if you prefer shredding later. Toss with 1/2 cup BBQ sauce until coated.
Add chicken and veggies: Pull the pan from the oven. Scoot the potatoes to one side and add the chicken pieces to the other.
Scatter sliced onion and bell pepper around, drizzling them with a touch of oil and a pinch of salt.
Roast again: Return the pan to the oven and roast 12–15 minutes more, until the chicken reaches an internal temperature of 165°F (74°C) and the potatoes are tender and caramelized on the edges.
Glaze with more BBQ: Brush or toss the cooked chicken with another 1/4–1/2 cup BBQ sauce for a glossy, sticky finish. If you like, broil for 2 minutes to get some char on the edges.
Warm the black beans: Heat the beans in a small pot or microwave until warm. Season with a pinch of salt and a squeeze of lime for brightness.
Assemble bowls: Add a generous scoop of sweet potatoes to each bowl.
Top with BBQ chicken, peppers and onions, warm black beans, cabbage, avocado, and cilantro.
Finish and serve: Drizzle with extra BBQ sauce. Add lime wedges on the side. For creaminess, spoon on a little Greek yogurt or sour cream.
Serve immediately.