Cabbage Slaw

This is from Salt Fat Acid Heat and it is a very bright take on cabbage salad.  I made this for a short rib dinner and it was a great accompaniment.

Quarter, core and thinly slice crosswise:
1 small head of red or green cabbage, about 1 1/2 lbs (680g)

Place sliced cabbage in a colander and season with:
2 generous pinches of salt 

Toss the sliced cabbage with your hands. To catch any water that gets drawn out by the salt, set colander inside a large bowl or pot. Set aside. Meanwhile, in a small bowl, combine:
1/2 small red onion, thinly sliced
1/4 cup lemon juice

Set aside for 20 minutes to macerate and take the bite off the onions.

After 20 minutes, drain any water the cabbage may have given up (it's fine if there's not much), then place in a large bowl along with the macerated onions (but not the oniony lemon juice, yet). Add to cabbage and onions:
1/2 cup roughly chopped parsley leaves
3 tablespoons red wine vinegar
6 tablespoons extra-virgin olive oil

Using your hands, toss well to combine. Take a pinch of cabbage and taste. Adjust, adding the macerating lemon juice and salt as needed. Finally, gently combine with the slaw:
  1 apple, cored and sliced into matchsticks, a couple of carrots shredded