Soak dried red chili peppers in hot water for 20 minutes. Reserve 3-4 tbsp of liquid. Soak dried shrimp in hot water for 10 minutes. Drain.
In a food processor, pulse all laksa paste ingredients and 3-4 tbsp of dried chili pepper soaking liquid until smooth. Heat 4 tbsp of oil in a skillet, cook the paste, keep stirring for about 4-5 minutes over medium high or until the oil separates from the paste. Set aside.
In a large pot over high heat, add chicken and enough water to cover the meat. Boil for 3 minutes. Remove the chicken from the pot, transfer it to a plate, and discard all liquid.
In a large clean pot, heat 3 tbsp of oil over high heat. Add shrimp shells and cook, keep stirring for 4-5 minutes. Add broth and drumsticks. Bring to a boil then lower the heat to medium-low, simmer gently, uncovered, for 30 minutes or until the chicken is fully cooked.
Remove the shrimp shells from the pot. Add laksa paste, fish sauce, and sugar. Simmer for 10 minutes.
Add coconut milk, tofu, and fish balls. Simmer until they are warm throughout for 10-15 minutes. Add shrimp and cook until they are fully cooked for about 3 minutes. Adjust seasoning with salt, sugar, or fish sauce if needed.
Serve with rice noodles, fish balls, shredded chicken, tofu, bean sprouts, cilantro, lime wedges, and sambal.