Preheat oven to 400°F.
In a large shallow Dutch oven over medium heat, melt the butter or olive oil.
Add the sliced onion and sauté for 5–6 minutes, until softened.
Add the garlic and cook for 1–2 minutes until fragrant.
Stir in the barbecue sauce, brown sugar, soy sauce, and chicken broth. Bring to a gentle boil, then reduce and simmer for 4–5 minutes to slightly thicken.
Turn off the heat. Remove a few spoonfuls of sauce and set aside for brushing later.
Season the split chicken breasts with salt and pepper.
Toss them in the sauce until fully coated. Arrange in a single layer, skin side up.