Preheat the grill to medium heat.
Brush the mushrooms with some oil and season them with salt and pepper, to taste. Grill until they are golden brown and soft, then transfer them to a serving bowl or platter. Drizzle with a few teaspoons of truffle oil, some of the baby arugula and shave a few pieces of Parmigiano over the mushrooms. Sprinkle with parsley and serve.