In a bowl, combine soy sauce and brown sugar. Add chicken thighs, ensuring they are well coated. Marinate for at least 30 minutes.
In a large pot, heat vegetable oil over medium heat. Add minced garlic and ginger, sautéing until fragrant, about 1 minute.
Remove chicken from the marinade (reserve the marinade) and add to the pot. Cook for 5-7 minutes until browned on all sides.
Pour in the reserved marinade, chicken broth, and water. Bring to a simmer, then reduce heat to low. Cover and let it cook for 20 minutes.
While the chicken is cooking, rinse the jasmine rice under cold water until the water runs clear. In a separate pot, combine rice with 2 cups of water and a pinch of salt. Bring to a boil, then reduce heat to low, cover, and cook for 15 minutes or until rice is tender.
After 20 minutes, check the chicken for doneness. If cooked through, remove the chicken and let it rest for a few minutes before slicing.
Serve the sliced chicken over a bed of jasmine rice, ladling the garlic ginger broth over the top. Garnish with sliced green onions.