Heat oven to 220C/200C fan/ gas 7. Cut the chicken wings into winglets by slicing through each of the joints. Keep the two meaty pieces and discard the wing tips, or freeze for stock.
Put the winglets on a large baking sheet, drizzle with the olive oil, then season. Roast in the oven for 20 mins, then reduce the temperature to 180C/160C fan/ gas 4 and cook for a further 25 mins.
Meanwhile, make the barbecue sauce. Put all the ingredients, except the butter, in a pan and mix together with plenty of black pepper. Let it bubble away for 3-5 mins to thicken up a little, then add the butter and stir until it has melted and made the sauce nice and shiny. Season to taste.
Half an hour before the chicken wings are ready, take them out of the oven and brush over three-quarters of the barbecue sauce. When they’re fully cooked, toss them in the rest of the sauce so that they become sticky.
In a small bowl, mash the blue cheese dressing ingredients together with some seasoning, until combined. The barbecue sauce and dip can be made a day ahead, covered and chilled. Serve alongside the wings with the celery sticks and radishes for dipping.