Heat oven to 425°F and position a rack in the center.
Trim fennel, remove cores, and cut into 1-inch wedges.
Toss fennel with olive oil, garlic, salt, pepper, lemon zest, and red pepper on a sheet pan.
Spread in a single layer, placing some wedges cut side down for browning.
Roast 20 minutes. Flip the pieces, then roast 10–15 minutes more until tender and caramelized.
Drizzle with lemon juice, sprinkle Parmesan and parsley, and toss to coat. Serve hot.