For the squash purée, heat the oil and butter in a large frying pan. Once the butter has melted add the squash and gently fry without colouring. Add the ginger and orange zest and cook until the squash is soft. Once softened, add the cream and season with salt and pepper.
Transfer the cooked squash to a blender and purée until smooth. Pass through a fine sieve into a clean pan to remove any lumps.
For caramelised apples, take a Parisian scoop and cut out spheres of apple and place them in a bowl of acidulated water.
Place a frying pan on the heat and add the butter and sugar. Once melted and the sugar had started to caramelise, drain the apple balls well and add them to the pan. Coat in the caramel, then remove them from the heat and set aside to cool.
For the duck glaze, boil the maple syrup, soy sauce and balsamic vinegar in a pan until reduced to a sticky glaze. Add the orange juice and reduce again.
Preheat the oven to 180C/160C Fan/Gas 4.
For the Derry duck, put the potatoes in a large saucepan and cover with cold water. Bring to the boil and cook the potatoes until soft but not falling apart. Once cooked, remove from the pan and refresh in ice-cold water to stop the cooking process. Carefully peel the cooled potatoes and set aside.
Season the duck breasts with salt and pepper, then fry them skin-side down in an ovenproof frying pan (you may need to do this in batches). Gently cook for about 8 minutes until caramelised all over and the fat has rendered from the skin. Pour the fat from the pan into small bowl. Transfer the duck to the oven and cook for 3 minutes.
Remove the pan from the oven and add the some of the glaze, coat the duck in the glaze, then set aside to rest for 10 minutes before serving.
Heat a large frying pan and add the butter, once melted add the chopped kale and toss to coat. Cook until the kale is tender, then season with salt and pepper.
Heat the duck fat in a separate large pan and add the peeled potatoes. Cook gently until golden-brown on all sides. Season with salt and pepper.
To serve, reheat the caramelised apples and squash purée. Spoon the purée onto serving plates. Slice the duck breasts and place next to the purée. Add the apples next to the duck and the wilted greens in the middle.