There is really not much more to it than I described. The amounts of the ingredients can vary and there isn’t one “right” ratio to follow. Here are some additional tips that might help, though I haven’t made a Holzfällerpfanne in a long time so no guarantee:

• Cut the potatoes thinly (only about a few millimeters), or else they will take forever and won’t be as crispy.
• Use a non-stick pan and a little bit of vegetable oil to prevent especially the potatoes and champignons from sticking.
• For cheese we always used shredded Gouda.
• When prepared right, the dish doesn’t need a lot of seasoning, I usually season it with pepper only, as the cabanossi itself has a lot of salt and the combination of the different ingredients make for a really balanced taste themselves.
• Don’t overthink the timing of when to add which ingredient. Excluding the cabanossi and onion you can’t really overcook neither the potatoes, champignongs nor apples.

I hope this helps! :)