Preheat the oven to 425°F and line a baking sheet with parchment paper so the sprouts roast evenly without sticking.
Slice the Brussels sprouts in half, then toss them with olive oil, salt, and pepper until they are well coated.
Spread the sprouts in a single layer on the baking sheet, making sure they are not crowded so they roast properly.
Roast in the oven until the sprouts become tender and develop golden brown edges, adjusting time based on their size.
Remove from the oven and toss with lemon juice, lemon zest, Parmesan, and thyme if using, so the flavors blend while still warm.
Garnish with fresh parsley and a pinch of red pepper flakes before serving for added flavor and color.