In a large bowl, combine the soy sauce, brown sugar, and a pinch of salt and pepper. Add the chicken thighs and marinate for at least 30 minutes, or up to 2 hours in the refrigerator for more flavor.
In a large pot, heat the vegetable oil over medium heat. Remove the chicken from the marinade (reserve the marinade) and place the chicken skin-side down in the pot. Sear for about 5-7 minutes until the skin is golden brown. Flip the chicken and sear the other side for another 5 minutes.
Add the minced garlic and ginger to the pot, stirring for about 1 minute until fragrant. Pour in the reserved marinade, chicken broth, water, rice vinegar, and sesame oil. Bring to a boil.
Reduce the heat to low, cover the pot, and let it simmer for 30 minutes, or until the chicken is cooked through and tender.
While the chicken is simmering, rinse the jasmine rice under cold water until the water runs clear. In a separate pot, combine the rinsed rice with 1 3/4 cups of water. Bring to a boil, then reduce the heat to low, cover, and cook for 15 minutes. Remove from heat and let it sit covered for 5 minutes.
Once the chicken is done, remove it from the pot and let it rest for a few minutes before shredding or serving whole. Taste the broth and adjust seasoning if necessary.
To serve, place a scoop of jasmine rice in a bowl, ladle the garlic ginger broth over the rice, and top with the chicken. Garnish with sliced green onions.