Prep: Preheat oven to 400°F. Toss sweet potatoes and onions with olive oil, spices, and salt on a lined sheet pan.
Roast: Bake for 20 minutes.
Add Chicken & Broccoli: Push potatoes to one side. Add broccoli (tossed with oil/salt) and chicken breasts. Brush chicken with ¼ cup BBQ sauce.
Finish Baking: Bake 15–20 minutes until chicken reaches 165°F.
Shred & Serve: Shred chicken, toss with remaining BBQ sauce, and divide into bowls.