Make the pad thai caramel: In a small saucepan, combine the brown sugar and ½ cup water and stir over medium-low heat until the sauce becomes as thick as caramel and develops a deep amber color, about 15 minutes.
Remove from the heat and let it cool slightly, then stir in the salt, white pepper, garlic, cilantro stems, fish sauce, and lime juice. Return the mixture to low heat and warm through, stirring until a smooth sauce forms, about 4 minutes. Remove the pad thai caramel from the heat and set aside.
Toss the Brussels sprouts with the oil and arrange them on a sheet pan cut side down. Roast, stirring every 10 minutes or so, until the sprouts are tender, golden brown, and charred in spots, 25–30 minutes.
Remove the Brussels sprouts from the oven and transfer to a large bowl. While they’re still hot, add the pad thai caramel and toss to combine. When the glazed sprouts have cooled slightly, add the bean sprouts, scallions, peanuts, and chile powder, then toss once more. Transfer to a serving plate and garnish with cilantro leaves. Serve with lime wedges.