For the parmesan fricos:
1) Preheat the oven to 180C/Gas 4.
2) Coarsely grate the cheese. Line a baking sheet with baking paper. Sprinkle about 10g of the cheese on the mat to make a thin disk, about 5cm wide. Repeat with the remaining cheese, spacing the disks evenly on the pan to make 8 fricos. Bake rotating the pan once during baking, until the cheese melts together and is just golden, about 12 mins. Cool fricos on the pan.
For the chicken and the dressing:
1) Position an oven rack 15cm from the grill and preheat.
2) Slice the mushrooms as thin as possible. Toss with the lemon juice and season with the salt and pepper, to taste.
3) Brush the chicken breast with olive oil and mustard. Season with the salt and pepper. Place the chicken in a gratin or casserole dish and grill, turning as needed until an instant-read thermometer inserted into the breasts registers 73C, about 25 mins. Transfer the chicken to a plate, reserve the pan.
4) Add the to the pan, and stir with a wooden spoon to release the brown bits that cling to the pan. Reserve the pan drippings.
5) Whisk the balsamic vinegar, salt, and pepper, to taste, in a large bowl. Gradually whisk in the oil, and the pan drippings starting with a few drops and then adding the rest in a steady stream, to make a dressing.
6) Slice the chicken. Toss the spinach and mushrooms with the dressing and divide among 4 plates. Scatter the chicken over the salads, top with the fricos and serve.