Preheat oven to 425°. Toss Brussels sprouts and 4 tablespoons oil on a rimmed baking sheet; season with salt and pepper. Roast, tossing once, until softened (but not soft) and browned, 20-25 minutes. Set aside.
Meanwhile, mix cornstarch and 1 tablespoon water in a small bowl until smooth.
Heat remaining 1 tablespoon oil in a medium saucepan over medium-high. Add garlic and ginger and cook, stirring often, until garlic is golden brown, about 2 minutes. Add chiles, soy sauce, sugar, vinegar, and ½ cup water and bring to a boil; stir in cornstarch slurry. Simmer, stirring, until sauce coats spoon, about 2 minutes. Let cool slightly.
Toss Brussels sprouts with sauce and serve topped with peanuts.
