Preheat the oven to 200°C.
Boil 4 tablespoons of water, honey, and salt in a saucepan, then remove from heat immediately.
Brush the glaze over the duck crowns and place breast-side up on a rack in a roasting tin.
Roast for 10 minutes at 200°C, then reduce heat to 180°C and roast for 20 more minutes.
Rest the duck in a warm place for 10 minutes after roasting.
Preheat a deep-fat fryer or pan of oil to 180°C.
Remove duck breasts from the bone and finish under a medium-high grill.
Deep fry the potatoes for 4 minutes until golden and drain on kitchen paper.
Boil peas with mint for 2 minutes and boil carrots and turnips for 3 minutes.
Pan-fry the boiled carrots and turnips in butter until tender.
Serve the duck with potatoes, vegetables, and the reduced duck stock.