Preheat oven to 425°F and line a large baking sheet with parchment paper.
Pat Brussels sprouts completely dry with paper towels, then toss with olive oil, salt, and pepper in a large bowl.
Arrange Brussels sprouts cut-side down in a single layer on the prepared baking sheet and roast for 20-25 minutes until deeply caramelized and crispy on the edges.
While Brussels sprouts roast, combine balsamic vinegar, butter, garlic, and Dijon mustard in a small saucepan over medium heat, simmering for 3-4 minutes until slightly thickened.
Remove Brussels sprouts from oven and immediately drizzle with balsamic glaze, tossing gently to coat before serving.