Preheat oven to 400F. Debone the chicken thighs, setting the bones aside, and season well with chili powder. Place on a baking tray lined with foil.
Bake for 50 minutes.
Meanwhile, place the chicken fat or olive oil in a pot over medium-high heat. Once hot, add in the chicken bones. Let these cook for at least 5 minutes, and then add in the broths. Season with salt and pepper to taste.
Once the chicken is done, remove the skins and set them aside for later. Add the fat from the chicken thighs into the broth and stir.
Make the BBQ sauce by combining all of the sauce ingredients.
Add the BBQ sauce to the pot and stir together. Let simmer for 20–30 minutes.
Use an immersion blender to emulsify the fats and liquids together. Shred the chicken thighs and add them to the soup. Simmer for another 10–20 minutes.