Preheat the oven to 400 degrees F.
Break apart the cauliflower into large florets and cut off the thicker stems. Set the cauliflower pieces stem side down in a 13 by 9-inch baking dish. Pour the wine and broth into the dish and drizzle olive oil over the cauliflower. Sprinkle with the oregano, and salt and pepper, to taste. Scatter the garlic over everything. Cover the pan with aluminum foil and bake until tender, about 30 minutes. The florets should fall apart if you poke them with your finger.
Meanwhile, stir the bread crumbs, chopped parsley, and 1 tablespoon olive oil together in a small bowl. When the cauliflower is tender, sprinkle the bread crumb mix and the cheese over the florets and put the dish, uncovered, back in oven until the topping is browned, about 15 minutes. Serve hot or at room temperature.