Preheat oven to 400°F. Line a baking sheet with aluminum foil.
Trim excess skin or fat from the chicken quarters and pat dry.
Brush the bottoms with olive oil and sprinkle with BBQ seasoning.
Place chicken skin-side up on the prepared baking sheet.
Brush the tops with the remaining olive oil and sprinkle with the remaining seasoning. Press the seasoning gently into the skin.
Bake for 35 minutes.
Generously brush the tops of the chicken with BBQ sauce.
Continue baking for 10–20 minutes, until the thickest part of the chicken reaches 175–180°F.
Turn the oven to broil and cook for 3–5 minutes, watching carefully so the sauce doesn't burn.
Remove from the oven and allow the chicken to rest for 5–10 minutes.
Serve and enjoy!