Preheat your oven to 400°F (200°C). Line a large, sturdy baking sheet with parchment paper or aluminum foil for easy cleanup. If using foil, lightly grease it with a small amount of cooking spray or olive oil. Ensure the baking sheet is large enough so the sprouts can be spread in a single layer.

Wash the Brussels sprouts thoroughly and remove any loose outer leaves. Trim the tough ends of the stems and cut the Brussels sprouts in half lengthwise, trying to keep the root end intact to prevent the leaves from falling off.

In a large mixing bowl, toss the trimmed sprouts with 2 tablespoons of the olive oil. Add the kosher salt and black pepper, and toss vigorously until every piece is lightly coated.

Create the Parmesan Crust Mixture: In a separate, small bowl, combine the finely grated Parmesan cheese, the remaining 2 tablespoons of olive oil, garlic powder, onion powder, dried Italian seasoning, and the optional red pepper flakes and flour. Stir until the mixture is thick and paste-like.

Add the Parmesan crust mixture directly to the bowl with the seasoned Brussels sprouts. Use your hands or a rubber spatula to carefully mix and coat each sprout half evenly. Ensure that the cut sides of the sprouts are heavily coated with the cheese mixture.

Arrange the coated Brussels sprouts on the prepared baking sheet in a single, even layer. Crucially, position them so that the cut side (the side coated with the cheese) is facing down against the baking sheet. This direct contact is essential for developing the deep, golden, crispy crust.

Roast for 12 to 15 minutes at 400°F (200°C) without disturbing them. Do not open the oven door during this period, as the cheese needs time to melt and crisp onto the pan.

Carefully remove the sheet from the oven. Using a thin, sturdy metal spatula, gently scrape under the sprouts and flip them over so the rounded side is now facing down. If the crust sticks, gently pry it up, ensuring the crispy cheese remains attached to the sprout. Return to the oven and roast for an additional 8 to 10 minutes, or until the sprouts are tender and the edges of the green leaves are charred and crispy.

Serve Immediately: Remove the baking sheet from the oven. Scrape the remaining crispy pieces of Parmesan crust off the sheet and mix them in with the sprouts. Serve immediately while they are hot and the crust is at its crispiest.