Remove the stems of the fennel and slice the bulb in half lengthwise. With the cut side down, slice the bulb vertically into 1/2-inch-thick slices, cutting right through the core. Spread the fennel slices on a baking sheet, coat with olive oil, salt, and pepper and toss with your hands.
Roast the fennel slices for about 1 hour, turning them once after 30 minutes, until the edges are crisp and brown. Remove from the oven and cover with Parmesan shavings. Taste for salt and pepper and serve.