Pat thighs dry. Heat oil in a wide heavy pot over medium heat and brown chicken skin-side down for 7 to 8 minutes, then turn and cook for 3 minutes. Spoon off excess fat, leaving about 1 tablespoon.
Add garlic around the thighs and cook for 1 minute. Pour in soy sauce, vinegar and water, then add bay leaves, pepper and brown sugar.
Bring to a gentle simmer, cover and cook over low heat for 30 to 35 minutes, turning once, until the thickest meat reaches 175 to 185°F and feels tender when pierced.
Transfer chicken to a platter. Simmer the sauce uncovered for 5 to 10 minutes until slightly reduced but still pourable, then remove the bay leaves.
Return chicken to the sauce for 1 minute, turn to coat and serve with the softened garlic and a small spoonful of sauce over each thigh.