Preheat oven to 425°F.: When you open the oven it should feel like a blast of dry, hot air, which encourages the outer leaves to crisp while the interior softens. A properly preheated oven ensures even caramelization across the pan. If the oven is not hot enough, the sprouts will steam and become limp rather than golden, so allow the full preheat time and consider using an oven thermometer to verify accuracy.
In a large bowl, toss Brussels sprouts with olive oil, melted butter, salt, garlic powder, and pepper until well coated. Add panko and 1/3 cup Parmesan, mixing to coat evenly.: You should smell the faint nuttiness of melted butter and the warm, savory hint of garlic powder as you toss. The oil and butter will sheen on the cut surfaces, signaling a good coat that will brown in the oven. Mixing in the panko breadcrumbs and part of the Parmesan cheese helps form a light crust that clings to the sprouts. A common mistake is overcrowding the bowl and not tossing thoroughly, which leaves pockets dry or underseasoned, so use your hands or tongs to ensure every piece is coated.
Spread sprouts on a sheet pan in a single layer, without overlapping. It’s okay if some panko and Parmesan fall off—just sprinkle any leftovers from the bowl over the sprouts.: When arranged correctly, each sprout sits alone and the hot air and pan surface can crisp the cut edges, creating browned, slightly blistered surfaces. You will hear a faint sizzle as they hit the hot sheet pan if it is preheated, which is a great signal. Overcrowding traps steam and prevents browning, resulting in soggy pieces, so resist the urge to pile them up; use a second pan if needed.
Bake for 18–23 minutes, or until the Brussels sprouts are browned, tender, and cheese is melted. Sprinkle with remaining 2 tablespoons Parmesan and any toasted panko left on the tray before serving. Best enjoyed right out of the oven!: During roasting you will notice their aroma shift from vegetal to toasty and slightly sweet, and leaves will develop dark golden patches. Test tenderness with a fork at about 18 minutes; the center should be soft while the edges are crisp. If they are not browning, slide them under the broiler for 1 to 2 minutes while watching closely. A frequent error is leaving them in too long which dries them out, so check early and often toward the end of cooking.
Sprinkle with remaining 2 tablespoons Parmesan and any toasted panko left on the tray before serving. Best enjoyed right out of the oven!: As soon as they come out, the last bit of Parmesan cheese will begin to soften, adding a salty finish and extra umami. The contrast between hot, tender centers and crisp, cheesy topping is most pronounced if served immediately. If you let them sit too long, the crunchy topping will lose its texture, so serve straight away for maximum contrast.