In a large bowl, combine the soy sauce, white vinegar, minced garlic, bay leaves, and black peppercorns. Add the chicken thighs and drumsticks, turning them to coat in the marinade. Cover the bowl and refrigerate for at least 30 minutes, or up to overnight for deeper flavor.
Heat the cooking oil in a large, deep skillet or Dutch oven over medium heat. Add the sliced onion and sauté for about 5 minutes, until softened and translucent.
Remove the chicken pieces from the marinade, reserving the marinade for later. Add the chicken to the skillet, skin-side down, and brown for about 5 minutes on each side.
Pour the reserved marinade over the chicken. Add the water and sugar (if using). Stir to combine.
Bring the mixture to a boil, then reduce the heat to low. Cover the skillet and let the chicken simmer for about 30 minutes, turning the pieces occasionally, until the chicken is tender and cooked through.
If the sauce is too thin, remove the lid and let it simmer uncovered for a few minutes to reduce and thicken slightly.
Serve the chicken adobo hot over cooked rice. Garnish with chopped green onions or fresh parsley, if desired.