Rub some salt into the skin of the duck breasts.
Put the breasts, skin-side down, in a cast iron frying pan and fry for about 8-10 minutes over medium-high heat or until the skin is golden brown. Flip the breasts over to sear them, then transfer them to a plate.
Meanwhile, chop the beetroot and onion. Rinse the blackberries.
Heat the oven to 180°C.
Discard most of the duck fat from the pan, then add the beetroot and onion. Fry for about 5 minutes, then add the oregano, a drop of water and the 2 Tbsp of balsamic vinegar. Cook for another 5-8 minutes, until the beetroot has become tender.
Transfer the mixture to an oven-proof dish. Scatter the blackberries on top and mix with a spoon. If the mixture is too dry add a splash of water or red wine (the blackberries will release their juice, so no need to add too much water).
Put the duck breasts on top, season with pepper and drizzle with the remaining balsamic vinegar. Bake for 10-15 minutes in the oven (depending on how well done you like your duck and how thick the fillet is).
Serve the duck with the beetroot and blackberry sauce.