Fill a large pot with water; add garlic, 15 ginger slices, spring onions, and 1 tablespoon sesame oil. Bring liquid to a boil. Carefully lower chicken into pot. Return liquid to a boil, reduce heat, and simmer over low heat until chicken is fully cooked, about 30 minutes. An instant-read thermometer inserted into the thickest part of the thigh, near the bone should read 165 degrees F (74 degrees C). Remove chicken from pot and transfer to a bowl of ice water, reserving chicken broth.
Combine 3 cups chicken broth, rice, 2 tablespoons sesame oil, pandan leaves, and 1 teaspoon salt in a rice cooker; cook according to manufacturer's instructions until rice is tender.