Remove fat from the chicken and reserve it for later use. Season chicken, inside and out, with salt.
Bring a large pot of water to a boil; add chicken, onion, 8 garlic cloves, sliced 1-inch piece ginger, salt, and white pepper. Bring liquid back to a boil, reduce heat, and simmer until chicken is fully cooked, 20 to 25 minutes. An instant-read thermometer inserted into the thickest part of the thigh, near the bone should read 165 degrees F (74 degrees C).
Carefully remove chicken and plunge into a large bowl of ice water until cooled. Remove chicken, dry, and cut chicken into bite-size pieces. Strain chicken broth and reserve liquid.
Wash and drain rice.
Heat reserved chicken fat in a skillet over medium heat; cook and stir 5 sliced garlic cloves and sliced 1/2-inch piece ginger until fragrant, about 1 minute. Add rice and oil; cook and stir until rice is coated in oil. Pour in enough reserved chicken broth to cook rice, about 6 cups. Add pandan leaves. Cover skillet and cook rice until tender and broth is absorbed, 20 to 30 minutes.
Pound red chile peppers using a mortar and pestle, adding a small amount of salt, until peppers transform into a fine paste. Stir enough lime juice into paste to make smooth; transfer to a serving dish.
Pound 4 garlic cloves and 1 slice ginger using a mortar and pestle until paste is formed; transfer to a separate serving dish.
Place lettuce leaves on a serving plate and arrange cucumber slices and tomatoes around dish. Place the chicken pieces in the center. Mix soy sauce and sesame oil together in a bowl; pour over chicken. Serve a bowl of reserved chicken broth on the side with a bowl of rice and the 2 dipping sauces.