Place onions, brown sugar, garlic, shrimp paste, galangal powder, coriander, cumin, anise seed, black pepper, and turmeric in the bowl of a food processor. Grind into a smooth paste. Transfer to bowl with chicken; mix well to coat chicken.
Cover the bowl with plastic wrap and marinate in the refrigerator for 24 hours.
Set oven rack about 6 inches from the heat source and preheat the oven's broiler. Line 2 baking sheets with aluminum foil.
Thread chicken onto bamboo skewers, leaving enough space to hold skewers. Arrange skewers on baking sheets.
Broil in the preheated oven until top is browned, about 10 minutes. Remove from oven; flip all the skewers over. Return to the oven and broil second side until browned, about 10 minutes more. An instant-read thermometer inserted into the center should read at least 165 degrees F (74 degrees C).