Preheat the oven to 180°C, fan 160°C, gas 4. Remove the skin from the chicken drumsticks.
In a large, flameproof casserole dish, heat the olive oil and fry the drumsticks until browned. Scatter the onions and garlic over the drumsticks, and cook until they have also browned.
In a seperate jug, make up 500ml chicken stock using the stock cube. Stir the Sainsbury's country vegetable mixture and stock into the casserole dish and season with a little salt and pepper. Bring to a simmer, then cover and transfer to the oven. Bake for 45 minutes. Leave to stand for 5 minutes before serving to allow the casserole mixture to thicken slightly.
Meanwhile, steam or boil the broccoli florets for 5 minutes, drain and serve with the casserole.