Wash chicken pieces and pat dry with paper towels. Season all sides with salt and pepper, then lightly coat in flour. Heat 3 tablespoons olive oil in a roasting pan over medium-high heat, then fry chicken for 3–4 minutes on each side until browned. Remove and set aside.
In the same pan with remaining cooking fat, fry diced onions over medium heat for 3–4 minutes, then add a pinch of sugar and cook for 1–2 minutes until caramelized. Add diced peppers, garlic, and mushrooms, then cook for 3–4 minutes, stirring occasionally. Stir in tomato paste and cook for 1 minute. Pour in white wine, passed tomatoes, and vegetable stock. Add paprika powder, salt, pepper, and herb stalks whole so they can be removed after cooking. Return chicken to the pan, add olives, and cover. Bake on the lower rack of a preheated oven at 200°C (400°F) for 60 minutes, until chicken reaches an internal temperature of 74°C (165°F).
Remove herb stalks. Taste and adjust seasoning with salt, pepper, and paprika as needed.
Serve with rice, dumplings, boiled potatoes, or baguette.