Preheat the oven to 400°F and position a rack in the center. For effortless cleanup, line a large rimmed baking sheet with aluminum foil.

Arrange the halved Brussels sprouts in the center of the baking sheet. Drizzle with olive oil and maple syrup, then season with salt and black pepper. Toss well to ensure each piece is evenly coated.

Spread the Brussels sprouts into a single layer, making sure the cut sides are facing down for enhanced caramelization. If the pan feels overcrowded, divide them between two baking sheets to allow proper roasting.

Roast for 15 minutes, then take the pan out of the oven. Drizzle balsamic vinegar over the Brussels sprouts and gently toss with a spatula to coat them thoroughly. This step encourages even browning.

Return the tray to the oven and continue roasting for an additional 8 to 10 minutes, until the Brussels sprouts are crisp on the outside and tender inside. If using two baking sheets, swap their positions in the oven after adding the balsamic vinegar. The outer leaves may appear deeply browned—this is the natural caramelization of the balsamic and maple syrup.

Remove from the oven and immediately sprinkle with crumbled feta or Parmesan, either on the baking sheet or after transferring to a serving dish. Serve hot for the best flavor and texture.