For the sauce, preheat the oven to 230C/350F/Gas 8.
Place the mallard carcass in a roasting tin and roast in the oven for 15 minutes, until browned.
Heat a large frying pan until hot. Add half of the butter to the pan and, when the butter starts foaming, add the shallots, garlic, bay leaf, thyme and freshly ground black pepper to the pan. Fry until well-browned.
Add the tomato purée to the pan and cook for a minute or two.
Add the red wine to the pan and cook until it reduces so much that nearly all of the liquid has gone.
Add the roasted carcass to the pan and stir well. Pour in the stock and 200ml/7fl oz of water.
Bring to the boil and then reduce the heat. Simmer over a low heat until thickened - this will take approximately 45 minutes.
Pass the sauce through a fine sieve into a clean pan or jug, and skim off any fat. Keep the sauce warm.
Technique: Skimming stock For the lentils, place the lentils in a saucepan with the stock, garlic, thyme and just enough water to cover. Cook them over a low heat for 20 minutes, until tender.
Drain the lentils and transfer them to a bowl. Cover with aluminium foil and keep warm until required.
For the duck, season the duck breasts well with salt and freshly ground black pepper.
Heat a large frying pan until hot, add the sunflower oil, and then the breasts, skin-side down.
Cook for 4-5 minutes, until crisp and brown. Turn the breasts over with tongs and cook on the other side for 2-4 minutes (this will leave the centre of each breast slightly pink; you may wish to add extra cooking time if you like your duck more cooked through).
Place the duck breasts on a clean plate, cover with aluminium foil, and allow them to rest in a warm place for at least ten minutes.
For the crisp parsnip shreds, heat the vegetable oil in a deep heavy-based saucepan to about to 190C/375F - a breadcrumb will sizzle and brown when dropped in it. (CAUTION: hot oil can be dangerous - do not leave unattended.)
Deep fry the parsnip slices until golden-brown. Remove them with a slotted spoon and place them in a bowl lined with kitchen paper to drain. Sprinkle with salt.
To serve, mix the salad leaves, balsamic vinegar and olive oil in a large bowl. Add the cooked lentils and combine gently. Carve the duck breasts into thin slices and add the duck to the bowl.
Carefully mix the salad together using your hands and divide among four plates, then drizzle over the sauce.
Top each mound of leaves with a handful of crisp parsnip shreds. Serve immediately.