In a large bowl, combine the soy sauce and brown sugar. Add the chicken thighs and marinate for at least 30 minutes, or up to 2 hours in the refrigerator for more flavor.
Heat the vegetable oil in a large pot over medium heat. Remove the chicken from the marinade (reserve the marinade) and sear the chicken thighs for about 5 minutes on each side, until browned. Remove the chicken and set aside.
In the same pot, add the minced garlic and ginger. Sauté for about 1 minute until fragrant.
Pour in the reserved marinade, chicken broth, water, rice vinegar, and sesame oil. Stir to combine and bring to a simmer.
Return the chicken to the pot, cover, and let it simmer for 20-25 minutes, or until the chicken is cooked through and tender.
While the chicken is cooking, prepare the jasmine rice according to package instructions.
Once the chicken is done, remove it from the pot and let it rest for a few minutes before slicing.
Serve the sliced chicken over a bed of jasmine rice, ladle the garlic ginger broth over the top, and garnish with sliced green onions.