Dry your chicken pieces with paper towels and season them with salt. Heat oil in a large pot, and once shimmering, add the chicken skin-side down. Sear until browned on all sides, about 6 minutes per batch. This step creates a rich flavor base for your adobo.
Remove the browned chicken and use the remaining fat in the pot to toast the garlic, bay leaves, and peppercorns. The heat releases their flavors, giving the dish its aromatic backbone.
Pour in water, soy sauce, vinegar, and oyster sauce. Stir well, scraping up any browned bits stuck to the bottom. These bits are full of flavor and add depth to the sauce.
Return the chicken to the pot in a single layer. Allow it to simmer uncovered until tender and cooked through, turning the pieces halfway. The flavors deepen as the sauce reduces.
While the chicken cooks, preheat your broiler and line a baking sheet with foil. Transfer the cooked chicken to the baking sheet and broil for a few minutes until the skin crisps. Brush with sauce and broil on the other side for a more flavorful finish.