Preheat the oven to 425 F. Spray a rimmed baking sheet with nonstick spray or line it with parchment paper or aluminum foil.
Place the Brussels sprouts on the baking sheet. Drizzle over the olive oil and sprinkle over the garlic and red pepper flakes. Sprinkle over the lemon zest or balsamic vinegar. Use your hands to toss the Brussels sprouts until they are evenly coated, and then spread them out in an even single layer on the baking sheet. Sprinkle with salt and pepper and roast for 15 minutes, until the Brussels sprouts start to soften.
Sprinkle over the Parmesan and use a spoon to toss the Brussels sprouts with the Parmesan until well combined, then spread them back out on the baking sheet. Roast for another 10 to 15 minutes until they are browned and tender. Taste and add additional salt and pepper as needed. Serve warm or hot.
Notes
Buying a domestic version of Parmesan is fine. If you are so inclined, buy Parmesan in chunks and grate or slice it yourself, or buy it in a market or cheese shop that grates their Parmesan regularly or has a high turnover of packaged grated Parmesan. Only buy it in the cheese case, never buy the stuff in shelf-stable cans.