First marination: Wash the chicken. Cut 3–5 deep slits into each piece. Season all over with ½ tsp salt and ½ tsp black pepper. Cover and rest at room temperature for a couple of hours, or refrigerate for longer.
Roast the sauce vegetables: Preheat oven to 450°F/232°C. Line a baking tray with parchment. Arrange the red bell pepper (cut side down), green chili, garlic cloves, onion layers, and scotch bonnets on the tray. Brush lightly with oil. Roast for 40 minutes, flipping halfway through, until wilted and lightly charred at the edges.
Blend the sauce: Transfer the roasted vegetables to a blender or food processor. Add the lemon juice, apple cider vinegar, oil, tomato paste, oregano, salt, black pepper, chili flakes, lemon zest, and cayenne. Blend until smooth.
Reserve, then marinate: Set aside ⅓ cup of the sauce for basting and dipping. Rub the remaining sauce all over the chicken pieces, working it into the slits. Cover and refrigerate for at least 2–3 hours, ideally overnight.
Bring to room temperature: Take the chicken out of the fridge 30 minutes before cooking. Preheat oven to 350°F/175°C.
Prepare the rack: Line a baking tray with parchment paper. Place a wire rack over it. Rub cold butter directly across the metal bars so the chicken won't stick.
Bake, baste, flip: Arrange the chicken pieces in a single layer on the rack. Bake for 40 minutes total. Every 10 minutes, pull the chicken out and brush both sides generously with butter and the reserved sauce, then flip. DO NOT skip the basting.
Rest: Remove from the oven and rest, loosely covered with foil, for 5–10 minutes. Internal temp should read 165°F/74°C at the thickest part of the thigh.
Make the creamy dip: Mix any leftover reserved sauce with the mayonnaise (or yogurt / sour cream). Taste and adjust — more salt, more mayo to mellow the heat, or a pinch of sugar for sweetness.
Serve: Serve hot with lemon wedges and your choice of sides — fries, rice, naan, coleslaw, or corn on the cob.