Put beets, potatoes and carrots in a pot and boil all the vegetables until fork tender but make sure not to over-boil. Beets will take longer than the rest. I recommend boiling them in a separate pot.
Meanwhile, take your washed cabbage and slice it discarding the core into bite-sized pieces. Then add your course salt and vinegar directly to the sliced cabbage and start squeezing it with your hands until it softens and releases some liquid. Cover it with a plate and put something heavy on top of it like a kettle full of water. Set aside for about 1 hour to let the vinegar work it’s magic. What we are trying to accomplish here is usually a long term marinating process but you are getting an abridged version.
When your potatoes, carrots and beets are cooked, cool them completely, then peel them, and dice them into little cubes.
Now take your cabbage and add the diced vegetables to it, do the same with pickles, onions and apples. Mix everything together and dress the salad with the olive oil. Taste it and add salt and pepper if needed. You might think that the salad is already salty enough because of the pickled cabbage and cucumbers.