Wash the beetroot well, leaving the skins on. Put into a saucepan of cold water and bring to the boil. Simmer until cooked through , starting to check with the tip of a knife after 40 minutes. Drain and rinse under cold water. When they are cool enough to handle peel off the skins using your hands.
In a large bowl whisk 1/2 tsp salt into the vinegar until it has dissolved. Whisk in the oil then check for seasoning adding some pepper and more salt if needed.
Grate the beetroot on the coarse side of a grater and drain well if it releases a lot of liquid. Do the same with the apple, discarding the core. Tip both into the bowl with the dressing, mix well then crumble over the nuts.