Heat oven to 425°F. Line a large baking sheet and lightly oil it.
Boil a big pot of well-salted water. Add Brussels sprouts and cook until just tender, 8–10 minutes.
Drain thoroughly, then pat sprouts dry so they crisp in the oven.
Toss sprouts with olive oil, melted butter, salt, pepper, garlic powder, smoked paprika, and red pepper flakes.
Spread on the sheet, leaving space. Press each sprout flat with a glass to about 1/2 inch thick.
Roast until browned and edges crisp, 15–20 minutes, flipping once halfway through.
Scatter Parmesan over the sprouts. Roast 3–5 minutes more until melted and golden in spots.
Finish with lemon zest and parsley. Taste and adjust salt, then serve hot.