Heat a wok or frying pan over a low heat and lay the duck breasts in the pan skin-side down. Reduce the heat to low and sizzle gently for 10-15 mins until the skin is golden and the fat has rendered into the pan. Remove the breasts to a plate and leave to cool.
With the pan still on a low heat, scatter the sugar over the leftover duck fat and stir in the curry paste and fish sauce. Cook, stirring, for 3-4 mins until fragrant, then add the aubergine and potatoes, and stir to coat. Let the veg absorb some of the paste for a few minutes, then pour over the coconut milk and half a can of water, add the lime leaves (if using) and bring to a simmer.
Meanwhile, finely slice the duck breasts. Stir the meat and resting juices into the curry and simmer for 40 mins, stirring occasionally, until the potatoes are just cooked and the duck is tender. Stir in the green beans and simmer for 10 mins more until the beans are cooked. Remove from the heat. Stir in the lime juice, taste and add more lime, sugar or fish sauce if needed. Scatter over the chillies, coriander and peanuts. Serve with cooked rice.