POSITION oven rack in bottom third of oven. Preheat to 425F.
TEAR large mushrooms in half, then toss with 2 tbsp oil on a baking sheet. Sprinkle with bread crumbs and grated parmesan.
BAKE in bottom third of oven until mushrooms are golden, 10 to 12 min.
WHISK vinegar with remaining 1/4 cup olive oil, honey and salt in a small bowl. Season with fresh pepper. Divide arugula among 4 dinner plates. Top with mushrooms and garnish with shaved parmesan. Drizzle with balsamic vinaigrette.