In a large bowl, whisk together the white vinegar, soy sauce, smashed garlic (6 cloves), kosher salt, ground pepper, and bay leaves to make the marinade.
Add the chicken to the marinade, cover the bowl with plastic wrap, and refrigerate for 20–30 minutes.
Remove the chicken from the marinade and reserve the marinade; pat the chicken dry with paper towels.
Heat the canola oil in a large skillet over medium-high heat. Brown the chicken on all sides until well browned, then transfer the browned chicken to a plate.
Add the thinly sliced onion to the skillet and cook over medium heat until very tender, about 5–6 minutes.
Add the minced garlic (4 cloves) and brown sugar to the onions, stir, and cook for about 30 seconds.
Pour in 1 cup of water and the reserved marinade, then bring the mixture to a boil.
Return the browned chicken to the skillet. Reduce heat to a simmer and cook uncovered until the chicken is cooked through and the sauce has slightly reduced, about 20–30 minutes.
Discard the bay leaves, adjust seasoning if needed, and serve the chicken with the sauce over rice. Garnish with chopped green onions.