Preheat oven to 200°C. Heat oil in a large ovenproof frying pan over high heat. Season chicken pieces all over and sear, skin-side down, for 4-5 minutes, turning occasionally, until golden all over and skin is crisp. Transfer chicken to a plate and reduce heat to medium-high.
Add butter, onion, garlic, pepper and anchovy to the pan and cook, stirring frequently, for 4-5 minutes until onion has softened and anchovy begins to break down. Add the wine, scraping the bottom of the pan with a wooden spoon, and simmer until wine is reduced by three-quarters. Stir in the stock and cream and bring to the boil. Skim off any fat that rises to the surface.
Add chicken pieces skin-side up and bake for 35-40 minutes until chicken is just cooked. Rest the chicken in the pan for 10 minutes, then remove from the sauce and place on a large serving platter with high sides.
Bring the sauce to a simmer over medium heat, skim off any fat that rises to the surface and stir in the cheeses until melted. Pour the sauce over the chicken and scatter with extra freshly ground black pepper to serve.
