Preheat the oven to 400 degrees F.
Place the separated pieces of maitake mushrooms onto a baking sheet and toss with a little olive oil and salt and pepper. Roast until crispy, 15 to 20 minutes.
Meanwhile, set a chop upright on a cutting board with the meaty side facing up. Using a thin sharp knife, cut into the meat and cut through the center, toward the bone. Stop short of the bone, then open up the meat like a book. Do not remove the meat from the bone; the bone itself will be at the center of the butterflied chop. Place the meat between sheets of parchment or plastic with a dab of water and gently and evenly pound the meat out with a meat mallet, flipping the meat a couple of times, until it's 1/4 to 1/8 inch thick. Season with salt and pepper.
Set up a dredging station: Line up 3 shallow bowls on the counter. Spread flour in one, beat the eggs in the second, and mix the fine bread crumbs, panko, Parm, nutmeg, and salt and pepper to taste in the third.
When the mushrooms are done, lower the oven temperature to 250 degrees F (leave the mushrooms in the oven). Place a wire rack over a rimmed baking sheet and set in the oven.
In large cast-iron skillet, heat about 1/4 inch oil over medium-high heat.
Coat the veal in flour and shake off the excess. Turn a chop in the egg, shaking off the excess, then press into the bread crumb mixture. Fry the chops, one at a time, until deep golden, about 3 minutes on each side. Keep the cutlets warm on the prepared baking sheet in the oven.
Serve the veal with lemon for squeezing and a side of mushrooms. Place the Arugula Salad with Sage and White Balsamic Vinaigrette under or on top of each cutlet.
In a small bowl, whisk the garlic, sage, shallot, lemon juice, vinegar, and honey. Still whisking, stream in the EVOO to emulsify. Season with salt and pepper. Put the greens and tomatoes in a large serving bowl, add the dressing, and toss to coat.