Preheat your oven to 425°F (220°C). Position a large rimmed baking sheet inside the oven while it preheats to ensure instant contact sear.
Trim the woody stems and blemished outer leaves off the Brussels sprouts. Slice each sprout in half lengthwise from top to stem and pat thoroughly dry.
In a large mixing bowl, toss the halved sprouts with olive oil, melted butter, minced garlic, sea salt, black pepper, and 1/4 cup of the grated Parmesan cheese.
Carefully remove the hot baking sheet from the oven. Arrange the sprouts cut-side DOWN in a single layer with space between each half. Do not overcrowd.
Roast undisturbed at 425°F for 20 to 25 minutes until the bottom flat edges develop a deep, caramelized crispy golden-brown crust.
Transfer hot sprouts to a ceramic serving dish. Shower immediately with remaining 1/4 cup Parmesan and chopped parsley, then finish with a zigzag drizzle of balsamic reduction. Serve hot!