Preheat the oven to 425°F (220°C). Line a very large sheet pan with parchment paper and set aside.
Pierce the sweet potato several times with a fork. Microwave on a microwave-safe plate for 5 minutes, flipping after 2½ minutes. Let cool slightly, peel, and chop into very small pieces.
Cut the chicken into 1/2-inch pieces. Remove stems and seeds from the peppers and coarsely chop. Trim and halve the green beans. Coarsely chop the broccoli.
Place the chopped sweet potato, chicken, bell peppers, green beans, and broccoli on the prepared sheet pan in an even layer.
In a small bowl, whisk together the olive oil, chili powder, paprika, granulated sugar, onion powder, garlic powder, ground cumin, cayenne, and salt.
Pour the seasoning mixture over the chicken and vegetables and toss with your hands or tongs until everything is evenly coated. Spread into a single even layer.
Bake for 10 minutes. Remove the pan, flip or stir the pieces to turn, then return to the oven and bake another 10–20 minutes until the vegetables are crisp-tender and the chicken is cooked through (about 20 minutes total for me).
If using cheese, sprinkle the shredded Cheddar over the hot pan and return to the oven 1–2 minutes until melted.
Serve the chicken and veggies over cooked rice or quinoa, and top with fresh cilantro and lime wedges if desired.