Combine garlic, chile pepper, shallot, turmeric, and kosher salt; bruise with a mortar and pestle, or with the flat side of a cleaver. Place into a bowl, and stir in brown sugar, and olive oil. Toss chicken wings with marinade, cover, and refrigerate for at least 1 hour.
Preheat oven to 400 degrees F (200 degrees C). Line a baking sheet with aluminum foil. Toss the chicken wings again to recoat in marinade, then spread out onto prepared baking sheet.
Bake in preheated oven until deep, golden brown, about 30 minutes.