Preheat oven to 180°C/Fan 160°C/Gas 4. Pat chicken dry with paper towels, then season all over with salt and pepper.
Heat 2 tbsp of the oil in a large oven proof pan over medium-high heat until shimmering. Cook chicken, turning occasionally, until it has rendered some of its fat and skin is golden brown all over, 7–10 minutes. Transfer chicken to a plate. You’ll have a pool of fat left in the pan. Spoon out all but 3 tbsp fat from pan.
Reduce heat to medium and add garlic and anchovies to the pan. Cook, stirring often, until garlic is softened and anchovies have disintegrated, about 2–3 minutes. Sprinkle in the chilli flakes, then stir in the tomato paste. Cook, stirring occasionally, until the tomato paste begins to split and stick to pan, about 3 minutes. Add the olives, wine, capers, bay leaves (if using), and lemon peel and bring to a simmer (still over medium heat). Cook, stirring occasionally, until most of the wine has evaporated, 5–7 minutes.
Snuggle chicken (skin side up) into sauce in a single layer. Pour in 250ml of water and bring to a simmer. Transfer the pan to the oven and bake, uncovered, until sauce is thickened and chicken is cooked through, 20–25 minutes (if using whole legs, it’ll take closer to 30–35 minutes). Taste a spoonful of the sauce—it should be salty enough between the anchovies and capers, so you most likely won’t need to season with more salt.