Melt the butter and oil in a large frying pan over medium-high heat. Add the drumsticks and shallots and cook for 5 minutes, turning until the drumsticks are well browned all over. Add the carrots, parsnips, capers, olives, lemon zest, oregano and honey.
Season with salt and freshly ground black pepper and stir well to combine then add the wine and let it bubble up, scraping the base of the pan with a wooden spoon to deglaze it.
Reduce the heat to medium-low, cover and cook for 20 minutes, stirring occasionally, or until the chicken is cooked through and the vegetables are tender. Squeeze the lemon juice over the dish then serve with mashed potato.
