1/3cupcrumbled feta cheese or 3 tablespoons Parmesan cheeseoptional
Place a rack in the center of your oven and preheat the oven to 400 degrees F. For easy clean-up, line a large, rimmed baking sheet with aluminum foil. Place the Brussels sprouts in the center of the pan and top with olive oil, maple syrup, salt, and pepper. Toss to coat.
Spread into a single layer on the baking sheet. For maximum crispiness, flip the Brussels sprouts so that the cut sides are touching the baking sheet. If your baking sheet is too small to hold all of the Brussels sprouts without crowding them, spread them between two pans.
Bake for 15 minutes, then remove the pan from the oven. Drizzle the balsamic over the top. With a spatula, gently toss to coat the Brussels sprouts with the balsamic and promote even browning, then return to the oven.
Continue cooking for an additional 8 to 10 minutes or until the sprouts are crisp on the outside and tender on the inside. (If you are roasting on two sheet pans, switch the pans' positions on the upper and lower racks after you add the balsamic). Don't be alarmed if the outsides of the Brussels sprouts become quite dark; this is the balsamic and maple syrup caramelizing.
Remove the pan from the oven and sprinkle with cheese, either directly on the sheet pan or after transferring the Brussels sprouts to a serving plate. Serve hot.
TO STORE: Refrigerate Brussels sprouts in an airtight storage container for up to 4 days.
TO REHEAT: Rewarm leftovers on a baking sheet in the oven at 350 degrees F.
TO FREEZE: I do not recommend freezing cooked Brussels sprouts, as their texture will be mushy once thawed.