Preheat oven to 400°F, dice sweet potatoes into 1/2-inch cubes, slice onion into 1/2-inch thick wedges, chop broccoli into 1-inch florets and leave the chicken breasts whole.
On a baking sheet tossed with 1.5 T olive oil, 1/2 t salt, 3/4 t garlic powder and 3/4 t chipotle powder, roast sweet potatoes and onion at 400°F for 20 minutes.
Remove sheet pan from oven, give sweet potatoes a quick toss, push them to the side of the sheet pan, toss broccoli florets with 1 T olive oil and 1/2 t salt on the cleared side and set whole chicken breasts on top. Spoon 1/4 cup of BBQ sauce on the chicken breasts.
Roast chicken and broccoli at 400°F for 15-20 more minutes, until chicken reaches 165°F internal temperature (at the thickest part when measured by a meat thermometer).
Remove chicken from the sheet pan, transfer to a cutting board, shred using two forks and place into a bowl with the remaining 1/3 cup BBQ sauce and black pepper, mixing it all together.
Serve by portioning sweet potatoes, onions and broccoli in each bowl, topped with shredded chicken mixed with BBQ sauce in Step 5, then finished off with fresh lime juice before eating everything while warm.