Rinse and drain farro. Add farro and broth to a saute pan or saucepan, bring to a boil, reduce to simmer, covered until tender to the bite, about 25 minutes. Remove from heat, drain any excess liquid, and allow to cool.
White the farro cooks, dice your apple, coarsely chop parsley, and slice cabbage as thin as possible, using a mandolin or a sharp knife. Combine ingredients in large bowl.
Sauté mushrooms with a generous amount of olive oil until tender, about 4 minutes. Add to farro, toss to combine. Grate Pecorino cheese into the farro, add salt and pepper to taste (careful, Pecorino is salty). I suggest using about 1/3 cup of the cheese so you don’t overpower the dish, but if you are in the mood for more, go for it.
Combine all ingredients for the dressing and whisk olive oil in until emulsified. Dress the salad, toss to combine, sprinkle with salt and cracked pepper.
Bring a pot of water to a boil. Reduce heat to a simmer, add 1 tbs vinegar and 1 tsp salt (white vinegar is customary but cider vinegar is fine if that is all you have). Crack egg into the center of the water gently. You can even crack the egg into a small cup first and slide it into the water gingerly. Make sure the water does not come back up to a boil, and I suggest doing this one egg at a time. Cook for 2-3 minutes for a runny center.
Using a slotted spoon, remove the eggs and place gently on a paper towel to soak up extra water.
Plate farro mixture, top with poached egg, and pile up the salad very last. Shave a few pieces of cheese on top and a few leaves of parsley for garnish. Serve immediately so egg stays runny and warm.