Preheat the oven to 425°F (220°C) and prepare a baking sheet with parchment paper. Halve the Brussels sprouts, drizzle generously with olive oil, and season with salt and pepper. Arrange them cut-side down on the baking sheet in a single layer. Roast for 20 to 30 minutes, or until the sprouts are tender with crisp, caramelized edges; roasting time will vary slightly depending on their size. Once roasted, if desired, toss the sprouts gently with the lemon juice, zest, Parmesan, and fresh thyme leaves. Finish with a garnish of fresh parsley and a light sprinkling of red pepper flakes before serving.